Is the will of God always fulfilled?

Simple answer - no.

We do know that God’s will is for all to be saved. 1Tim 2:4.

We also read about a second death Rev 20:6. This means that there will be some who, for reasons unknown at this point, will not be saved. God has provided the same gracious sacrifice to cover their sins as any other person, but they must have rejected, or otherwise excluded themselves from eternal life.

So while God’s will is for all to share eternity with Him, some will obviously not.

nevertheless not what I will, but what thou wilt. Mark 14:36

Jesus explained that his will was different from God’s. In other words, Jesus’ will was not God’s will - they were not the same. Jesus had to choose to live out God’s will and suppress his own will.

Some like to obfuscate and say that Jesus always did God’s will, but that is missing the point entirely of what Jesus expressed.
Jesus did not have God’s will, he had another will.

It is his perfect obedience to God’s will that enabled him to be the Lamb, thus keeping God’s will for all men. In grace we are included in his obedience.

There are actually two layers of what we may see as the Will of God:

The "Physical" Layer:

The principal laws of God are set. They are immutable. They comprise what we observe as "Natural laws", including biology (if someone is injured or murdered, his body is dead, even if the person was very good-hearted and pleasant before God's commandments). These laws are beyond "good" and "evil" and neither we nor even God can/will break them.

The Human Layer

God's commandments are given for good inside these immutable laws. It contains the notion of "good" and "evil" with respect to the best fulfillment of the possibilities of the universe of Him, and pointing to the final, ideal realisation of His creation which is the Kingdom of God prophesied by Jesus (peace be upon him). The commandments, the recommendations, can be and are broken.

Our world and the Kingdom to Come

We live in a world where only the first layer is immutable. The commandments are a hint and a challenge to us to be prepared for the Final Kingdom, to save and protect this world and to train ourselves to be apt to live in that future, ideal world, where both layers of the Will of God are law.

(This answer may become off-topic pending clarification of the question) With regards to the will of God, the common view among Protestants that I have encountered, and which I also hold, is that there are 2 categories of what we refer to as "God's will". On the one hand, you have what God desires as part of His perfect nature; his perfect will, that which reflects a perfect state of affairs. In this sense, God does not desire, or "will", eg sin, the Fall etc.

On the other hand, you have what is called God's antecedent will, decreed will, or most simply, His Plan. This refers to what God has decided will be the course of reality, past present and future.

The latter aspect of God's will, His plan, never fails, nor is it ever thwarted, but unfolds exactly as He has planned down to the movement of the smallest atom. However, there are parts of His plan which clearly seem to go against His perfect will, eg sin, death, all the bad stuff. Different denominations have different explanations of why this apparent discrepancy is present; I believe free will is a sufficient explanation. God simultaneously desires us to freely love Him and come to him - which requires free will - and sinlessness, which are logically incompatible; freedom to make bad choices will inevitably result in bad choices being made. However, He deemed the meaningful relationships we would be able to have with him more valuable and glorifying to Himself than creating a billion perfect robots.

Is the will of God always fulfilled?

The short answer is no.

The will of God has has several meanings, and in one sense we know that God's will is not always done, simply because we do not always do it! Any one who says he has never sinned is a liar. Sometimes we sin and rebel against His will. Jesus also taught us to pray: "Thy Kingdom come, Thy will be done," which certainly implies that His Father's will is not always done at every moment otherwise, why would we need to pray that it might be done.

Saint Paul alludes to this in Ephesians 1:9-10:

"For He has made known to us in all wisdom and insight the mystery of His will, according to His purpose which He set forth in Christ as a plan for the fullness of time, to unite all things in Him, things in heaven and things on earth."

God's antecedent will is obviously not fully accomplished, because some of His creatures, whether they are man or demons, misuse the freewill He gave to them, and reject the loving plan that He had originally laid out for them.

God's moral will is obviously not always done. As a result, God's consequent will which is to defeat Satan and the demons in the end. In the meantime, He sends His Son to earth to redeem us on the Cross from our moral debt due to God for our sins and to merit for us by His perfect life and death all the sanctifying graces that we need to overcome the power of sin in our hearts and to prepare us for everlasting life with Him in heaven.

God's consequent will is fully done when souls freely respond to and cooperate with His grace: when they repent, are converted, and live out their faith in works of loving service, on the road to heaven. But God's consequent will, in this sense, is not always done either, because some people refuse to repent and cooperate with the merciful love of Jesus Christ. Some souls simply refuse to turn towards God and his Divine Mercy.

“Thy will be done” is one of the requests in the Lord’s Prayer. In part, Jesus taught His disciples to pray, “Our Father in heaven, hallowed be your name, your kingdom come, your will be done, on earth as it is in heaven” (Matthew 6:9–10). Jesus Himself pleaded for God’s will to be done in the Garden of Gethsemane. Prior to His crucifixion, He prayed, “My Father, if it is possible, may this cup be taken from me. Yet not as I will, but as you will” (Matthew 26:39). Jesus was committed to seeing God’s will accomplished, and the prayer “Thy will be done” was a theme of His life.

Most simply, to pray, “Thy will be done,” is to ask God to do what He desires. Of course, we’re praying to the God who said, “Let there be light,” and there was light (Genesis 1:3), so we know that His sovereign decree will be accomplished, whether or not we pray for it. But there is another aspect of God’s will, which we call His “revealed” will or “preceptive” will. This is God’s “will” that He has revealed to us but that He does not force upon us. For example, it is God’s will that we speak the truth in love (Ephesians 4:15) and that we not commit adultery (1 Corinthians 6:18) or get drunk (Ephesians 5:18). When we pray, “Thy will be done,” we are asking God to increase righteousness in the world, to bring more people to repentance, and to further the cause of the kingdom of His Son.

The Lord’s Prayer begins by acknowledging God as Father in heaven. Jesus then models petition, presenting three requests to the Father: 1) That God would cause His name to be hallowed; in other words, as Albert Mohler explains, “that God would act in such a way that he visibly demonstrates his holiness and his glory” (The Prayer That Turns the World Upside Down: The Lord’s Prayer as a Manifesto for Revolution, p. 61). 2) That God would bring His kingdom to earth; that is, that the preaching of the gospel would convert sinners into saints who walk in the power of the Holy Spirit and that God would rid the world of evil and create the new heavens and new earth where God will dwell with His people and there will be no more curse and no more death (see Revelation 21—22). 3) That God’s will would be done “on earth as it is in heaven” (Matthew 6:10). In heaven, the angels perform God’s desire completely, joyfully, and immediately—what a world this would be if humans acted like that!

As a point of clarification, “Thy will be done” is not an impassive prayer of resignation. Jesus’ prayer in Gethsemane was not passive or fatalistic in the least; He bared His heart before the Father and revealed His ultimate desire: for God’s will to be accomplished. Praying, “Thy will be done,” acknowledges that God has more knowledge than we do and that we trust His way is best. And it is a commitment to actively work to further the execution of God’s will.

Romans 12:1–2 says, “Therefore, I urge you, brothers and sisters, in view of God’s mercy, to offer your bodies as a living sacrifice, holy and pleasing to God—this is your true and proper worship. Do not conform to the pattern of this world, but be transformed by the renewing of your mind. Then you will be able to test and approve what God’s will is—his good, pleasing and perfect will.” Understanding who God is, we submit ourselves to Him and allow Him to transform us. The more we know God, the more readily our prayers will align with His will and we can truly pray, “Thy will be done.” We can approach God in confidence that “if we ask anything according to his will, he hears us” (1 John 5:14–15). - What does it mean to pray, “Thy will be done”?

Jesus’ words in the Garden of Gethsemani shows us the fear Our Lord had in his human nature. In all things Jesus was like us except he never sinned.

And he said, Abba, Father, all things are possible unto thee; take away this cup from me: nevertheless not what I will, but what thou wilt. - Mark 14:36

Thus the will of God always is not fulfilled while we are hear on earth?

So the short answer is ”no”.

Ultimately, God's will shall be done totally, everywhere, by everyone, as Jesus told his followers to pray: "Our Father who art in heaven, hallowed be thy name. Thy Kingdom come. Thy will be done on earth as it is in heaven" (Matthew 6:9-10). A day is coming when everything in all creation will bow before the King of Kings - Philippians 2:9-11.

The fact that a few billion people on earth have not done God's will in their life-times, and that there are hosts of rebellious spirit creatures actively resisting God's will over the millennia until Revelation chapter 20 is fulfilled has no bearing on the answer. God is Sovereign, the Almighty, and his will shall be done.

It is a red herring to bring up Mark 14:36 as we know that Jesus did submit to God's will, to die on a cross. Nor was he forced to carry God's will out to the end. However, had it turned out to be God's will for his Son not to die on a cross, then something else would have happened, as the account of Abraham about to sacrifice his miracle-child but being prevented once his faith had been tested shows us. With Jesus in the garden of Gethsemane, however, this wasn't 'just' a test of faith; this was the fulfilment of the prophecy in Genesis 3:15 being worked out, and it was, indeed, worked out to its spectacular conclusion - the resurrection of the crucified Christ - just as the scriptures had foretold.

Nothing in all creation could have thwarted God's will for that, the triumph over sin, death and the devil, because God's promises are totally dependable. Let anyone find an example of any of God's promises not being fulfilled, and then you might have cause to question the invincibility of God's perfect will. Everything in creation is working towards the final fulfilment of the final promises, whether people or demons realise that or not. God's will shall be done on earth, as it is in heaven, when 2 Thessalonians 2:1-14 is fulfilled, which harmonises with the promises in Revelation chapter 20, and elsewhere.

Take particular note, please, of how it is God's will to cause those who do not love his truth, to be deceived and to perish - 2 Thess. 2:9-12. They might think they are thwarting God's will, and that they are exercising their precious 'free will' which God is impotent to stand up against, but they should read Revelation chapter 16 to see the invisible demonic powers that are deceiving them. God has revealed his will to humanity, and a day will come when all will know that he has accomplished it, just the way he said he would.