Why Fermat Is Right

The wiki article I was reading:
https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem

If you can intersect or inject the hypercube mathematics shown here, then you can do a feasible form of Fermat's Last Theorem:
http://mathworld.wolfram.com/Hypercube.html
http://www.magic-squares.net/c-t-htm/t_math.htm

You cannot do it unless you apply it to a hypercube.
Fermat is right about non-hyper space.
Likewise, the next question would be, would such an iteration even be meaningful?