Jeremiah 32:17 says of God, "Nothing is too difficult for you." God created the trees, seas, all that we can see and we say with Jeremiah, there is nothing God cannot do. I believe that. But at the same time I would say there are things that God will not do.
God will not sin. He is pure, holy and righteous. He says in Leviticus 11:44, "I am your God. Be holy, for I am holy." God has never and will never allow sin to enter his life or alter his character.