In which suttas does The Buddha cover annihilationism (ucchedavāda)?

perhaps you will find what you want in the vagga about wrong views http://obo.genaud.net/backmatter/indexes/sutta/sn/03_kv/idx_24_ditthisamyutta.htm

Some people hold the common fatal wrong view -- see DN2 -- "fatal" because headed to hell, driving them more to make their believes real as only escape option having:

'Great king, there is nothing given, nothing offered, nothing sacrificed. There is no fruit or result of good or bad actions. There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no brahmans or contemplatives who, faring rightly and practicing rightly, proclaim this world and the next after having directly known and realized it for themselves....Its eulogies are sounded only as far as the charnel ground. The bones turn pigeon-colored. The offerings end in ashes. Generosity is taught by idiots. The words of those who speak of existence after death are false, empty chatter. With the break-up of the body, the wise and the foolish alike are annihilated, destroyed. They do not exist after death.'

Even: "To be or not to be, is no question", Buddhadasa told seldom once wisely.

At large: vibhava-driven, desire for not being, becoming, is all more or lesser common with the self/actor-denying view.

Third, the way “self” (attā) is defined in the annihilationist views (51–57) shows that the concept of self in the Buddha’s time did not—contrary to what is often believed—always have to mean an eternally existing self. In each of these views, the self is defined in such a way that it will be annihilated at death.

As not willing to correct their habits, wishing that kamma will not fall on them, they are hoping that "‘I might not be, and it might not be mine. I will not be, and it will not be mine.’"

Otherwise they would really see them in big troubles, if causes may have effects on them, facing such even after the break-up of the body.

As the Brahma-net sutta gives, they are mostly eager to gain certain "sunnata" by practicing Jhana, if not simply holding the common view that they are here only because mother and father.

56. “Another says to him, ‘There is, my good man, that self of which you speak. I don’t say that there’s not. But it’s not to that extent that the self is completely exterminated. There is another self where—with the complete transcending of the dimension of the infinitude of consciousness, ...(perceiving,) ‘There is nothing’—one enters & remains in the dimension of nothingness...[27] You don’t know or see that, but I know it, I see it. When this self—with the breakup of the body—is annihilated, destroyed, & does not exist after death, it’s to this extent that the self is completely exterminated.’

Or they mix it up (as very popular today under householders of various livelihho) with the Uposatha of the Jains, the no-self approach on sessions.

"I am nothing by anything or of anything. Thus there is nothing by anything or of anything that is mine."' Yet in spite of that, his parents know of him that 'This is our child.' And he knows of them that 'These are my parents.' His wives & children know of him that 'This is our husband & father.' And he knows of them that 'These are my wives & children.' His workers & slaves know of him that 'This is our master.' And he knows of them that 'These are my workers & slaves.' Thus at a time when he should be persuaded to undertake truthfulness, he is persuaded to undertake falsehood. At the end of the night, he resumes the consumption of his belongings, even though they aren't given back to him. This counts as stealing, I tell you.

It's the most common view under "modern/western" "Buddhists", this Annihilationists, some working on reaching such, some thinking that what ever doing, it will not fall to back on me, giving the fathers and mothers, or mother nature, the origin of causes of experiances (who ever might have them...).

...“There, where any of those contemplatives & brahmans who are annihilationists proclaim the annihilation, destruction, & non-becoming of an existing being on seven grounds: That they would experience that other than through contact isn’t possible... “But when a monk discerns the origination, ending, allure, drawbacks of, & emancipation from the six sense media, he discerns what is higher than all of this.

See also natthikaditthi, one of the evil views, taught by Ajitakesakambala and further recourse found there.

Good to take on the safe bet

(Not given for trade, exchange, stacks of short time benefit in this life, but for even the next and beyond)