So mostly this is me brainstorming and spewing it out into a public space.

Given N items, what is the ‘most cubic’ shape you can make with it?

Rules: The result must be a *rectangular column* in three dimensions.

The ideal result is a cube, but that is only possible for cubic numbers (1,8,27, etc), or N^{-3}`*`

N^{-3}`*`

N^{-3}

the middle result is a column X`*`

X`*`

Y,

the worst result is a column 1`*`

1`*`

N.

The best case and worst case are trivial. What’s the best algorithm for the middle case?

Starting at X = Floor(N^{-3})?