The apocryphal story is told of a Sunday School teacher who asked his class, “If you tell me something God can do, I’ll give you an apple.” To which a wise little girl responded, “If you tell me something God can’t do, I’ll give you a case of apples!”
Well, in actuality, there are things God cannot do, as Stephen Charnock noted when discussing the omnipotence of God:
The power of God is that ability and strength whereby he can bring to pass whatsoever he please, whatsoever his infinite wisdom can direct, and whatsoever the infinite purity of his will can resolve.
[But] Some things are impossible to the nature and being of God…He cannot die who is life itself…God cannot do anything unbecoming his holiness and goodness…any unrighteous thing. God cannot love sin…The will of God cannot will anything but what is worthy of him…It is impossible for God to lie (Heb. 6:13); God cannot deny himself (II Tim. 2:13), because of his faithfulness…God is omnipotent, because he cannot do evil and would not be omnipotent if he could.
Words of Grace 