Excerpts from internet.cube-lovers: 10-May-91 5by cubes Andy
Latto@lucid.com (383)
You can't make an order 21 cube, or any cube of order 7 or higher.
When you turn the top layer of such a cube by 45 degrees, the corner
cubie will not touch the other layers at all, so there's
no way to keep it attached, and it will fall off.
There is no law that says that the cubes have to be the same size.
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JUST AS AN EXAMPLE.