Hypercubic numbers

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Since cube numbers refer to 3-dimensional figurate numbers, hypercube numbers refer to n-dimensional figurate numbers for n greater than 3.

Cubic numbers refer to algebraic numbers of 3^rd degree, and hypercubic numbers would/should then refer to algebraic numbers of n^th degree for n greater than 3, but there is no such usage...

So, you probably meant hypercube numbers.