Nicomachus's Theorem

Theorem
In general:
 * $\forall n \in \N_{>0}: n^3 = \paren {n^2 - n + 1} + \paren {n^2 - n + 3} + \dotsb + \paren {n^2 + n - 1}$

In particular, the first term for $\paren {n + 1}^3$ is $2$ greater than the last term for $n^3$.