On the other hand, I would be willing to pay a fair amount of money for
an order 21 cube. :-)

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.

Andy Latto
latto@lucid.com