Is Buddha a source of suffering?

Depends on which version of Buddha you're talking about, the unenlightened prince Siddhartha, or the enlightened Tathagata?

"What do you think, monks — Is form constant or inconstant?"

"Inconstant, lord."

"And is that which is inconstant easeful or stressful?"

"Stressful, lord."

"And is it fitting to regard what is inconstant, stressful, subject to change as: 'This is mine. This is my self. This is what I am'?"

"No, lord."

"...Seeing thus, the well-instructed disciple of the noble ones grows disenchanted with form, disenchanted with feeling, disenchanted with perception, disenchanted with fabrications, disenchanted with consciousness. Disenchanted, he becomes dispassionate. Through dispassion, he is fully released. With full release, there is the knowledge, 'Fully released.' He discerns that 'Birth is ended, the holy life fulfilled, the task done. There is nothing further for this world.'" ~~ SN 22.59 ~~

Buddha is also a source of suffering

i think it depends, if you are not getting the essence of what Lord Buddha said. Just following other stuff like this very question. And some debates on those days social environments. Then, yeah it also will be source of suffering. Other than that if someone think such way then he or she tend to refuse almost everything what Buddha said, eventually they will become so called FREE THINKERS. Arises of this so called FREE THINKERS will be the end of pure Buddhism.

I think that the Agama you quoted -- here -- is intended to teach that the Dharma (or Dhamma) is unconditioned.

Whether a Tathāgata arises in the world or not, this element of dharma remains unchanging.

In other suttas the Dharma is also described as "timeless" (or perhaps "ever-present" or "continuous" depending on how akalika is translated).

Note too that "the Dhamma" is described as "a dhamma" -- it's not a "sankhara", (i.e. not a compound thing or composite thing). The Dhamma says that it's sankharas (not dhammas) that are impermanent. Nibbana is an example of a not-impermanent dhamma.

Back to the Buddha:

• When asked whether the Tathagata exists or doesn't exist after death, I think that the canonical answer was:

  • It's inappropriate to associate the Tathagata with the aggregates
  • You're therefore unable to identify the Tathagata even when he's alive

• In the time leading up to the Buddha's parinibbana, some of his attendants (e.g. Ananda) seemed reluctant to accept that.

  Then the Venerable Ananda went into the vihara and leaned against the doorpost and wept:

  "I am still but a learner, and still have to strive for my own perfection. But, alas, my Master, who was so compassionate towards me, is about to pass away!"

  Maybe that (i.e. their attachment) was a source of suffering.

• In various suttas, we're told to associate the Buddha with the Dharma -- for example, SN 22.87:

  For a long time, Lord, I have wanted to come and set eyes on the Blessed One, but I had not the strength in this body to come and see the Blessed One."

  Enough, Vakkali! What is there to see in this vile body? He who sees Dhamma, Vakkali, sees me; he who sees me sees Dhamma. Truly seeing Dhamma, one sees me; seeing me one sees Dhamma.

  This doctrine is developed or repeated in later forms of Buddhism (see dharmakāya).

So to the extent that the Buddha is the Dharma, and to the extent that the Dharma is unconditioned and timeless, I wouldn't view the Tathagata as conditioned.

I think I also associate with the Tathagata with Nibanna -- as an answer to any question like, "where is the Tathagata?" and "what does he experience?" -- and that (Nibbbana) isn't "suffering" either.

If I want to posses or be Buddha then I will suffer.

Maybe so.

I guess that Siddhartha Gautama discovered or realised something similar, during his search for enlightenment -- something like, "When I want to become enlightened, I suffer. To be enlightened, you have to stop wanting (craving and attachment)."

I think that's explicit in some suttas like the Brahamana Sutta (in that sutta, "going to the park" might also be a metaphor for becoming a monk ... because in those days, monasteries were just parks -- "forest monasteries").

And I think there are doctrines and practices in Mahayana to try to get over that (perhaps, I'm not sure, the "original nature" or "Buddha nature" doctrine; not to mention "tantrayana").

Maybe you're projecting something (is "projection" a concept in Buddhism?)? -- see this answer where someone starts by wanting to see himself as a good monk, the best monk ... later, perhaps more maturely, as "just a monk". Should even the Buddha, as a person, be seen as "a monk"?

But anyway if you think that "wanting to be Buddha" and so on is problematic you might find it less uncomfortable to identify as "a Buddhist" rather than "a Buddha" -- see for example this answer; or, this answer summarising different forms of buddhism.