http://en.wikipedia.org/wiki/Squared_square(adsbygoogle = window.adsbygoogle || []).push({});

It is known that simple perfect squared squares exist, with the lowest one being of order 21. It is also known that no simple perfect cubed cube exists, for the smallest cube would, again, require cubes atop it that form another squared square, which would require yet another, and so on.

However, can it be shown that a simple perfect cubed rectangular prism exists? Or, that merely a compound perfect cubed rectangular prism exists?

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# Squaring the Square -> Cubing the Rectangular Prism

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