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I assume the goal is to make a rectangle? Does it have to be a square?

Rectangle, not possible to make a square. (Count the area and try and find integer width & height that fits)

But two squares is possible (8x8 with a negative 2x2 anywhere inside, including at the center)

Yes, the goal is to make a rectangle. It cannot be one giant square as there are 60 (5 x 12) mini squares.