There are a lot of things that God cannot do, by his very nature. For example, God cannot lie (Numbers 23:19, Hebrews 6:18). God cannot commit an unloving act. God cannot act unjustly. God cannot do an unholy thing.

God is much more consistent in himself than we are. One could even claim (probably an exaggeration) that there are more things humans can do than God can do because we are inconsistent and we can do things which violate our beliefs. We can do one thing one day and then a completely contradictory thing the next. God never acts this way. We can lie. God cannot. We can treat other people with hatred. God cannot. We can be unjust. God cannot.

My conclusion is that God cannot do anything which violates his nature. There are many things that God is… God cannot do anything which violates what he is…

The typical (and really rather shallow) example used by skeptics is that God cannot create a rock so big he cannot lift it. By his nature, since God is omnipotent, then he cannot create a thing he cannot lift. To do so would be to make him not be omnipotent, but he is omnipotent, therefore he cannot do this thing.