There are many things God cannot do—things related to His character rather than His ability. The Bible makes it clear that God cannot lie. (See Heb. 6:18 comment.) He cannot sin. He also cannot let injustice go unpunished. As for whether God can create a rock that He cannot lift, when it comes to the ability of God, nothing is impossible.
However, this question reveals a lack of common sense. The questioner thinks that if God couldn’t create a rock too big for Him to lift then He is not omnipotent. Then again, we could ask if God could make a square peg and put it into a round hole, and make it fit perfectly. Or, could God make an egg that is not an egg?
These questions are asked to divert attention away from the real issue. But it seems that God had the atheist pegged thousands of years ago when He said, “Do not answer a fool according to his folly, lest you also be like him” (Prov. 26:4).
Here is one more “nonsensical” question that may make sense: Could God take a man who is a fool but thinks that he’s wise, and make him see that he is a fool, so that he will be wise? The answer is in 1 Cor. 3:18.
Psalm 38:4 For my iniquities have gone over my head; Like a heavy burden they are too heavy for me.