I have thought about this problem for a while and I have decided that it is impossible to answer this question, because there is a fault in the question itself.

Asking if God can make a square circle reminds me of an old paradox I once heard - "Can God make something He cannot lift?", the paradox being that if He can make it, there is something He cannot do (i.e. lift the unliftable object) and if He cannot make it, that is also something He cannot do.

As with most paradoxes, there is something wrong with it. It is like asking what would happen if an unstoppable cannonball hit an immovable wall. *These two things are mutually exclusive!

If we assume for a moment that God exists and is all powerful, then the thing He cannot lift is logically incoherent. It does not exist, yea, it cannot exist. It is a logically impossible thing to comprehend, as if one esists (God) the the other cannot (The object)

Therefore He cannot create it, but not merely because He is not all-powerful, but because it is a logically incoherent thing to exist.

You could apply this thinking to the square circle problem. The definitions of a square and a circle are so different that one oblect cannot be both at the same time. These two definitions of the object are mutually exclusive.

If it is a square, it is evidently not a circle. Part of the definition of a square is that it is not a circle, and vice versa.

Therefore it does not matter whether God could not create this object because it is a logical impossibility, and CANNOT exist, QED.