Oh, no, 128, as you said earlier - that pic is a top view, the whole thing is 4 layers high. So there are 64 in the cube, 64 in the wall which defines the square.
I was just showing this could be made to work and still have the square touching the faces of the cube.
Yet FFF says this is not the answer.
FFF, when people are done, please post the official answer and we can have another puzzle trying to figure out how they reached it.
I really should go do stuff. See all yall later.