Cube as Sum of Sequence of Centered Hexagonal Numbers

Theorem

 * $C_n = \ds \sum_{i \mathop = 1}^n H_i$

where:
 * $C_n$ denotes the $n$th cube number
 * $H_i$ denotes the $i$th centered hexagonal number.

Proof
From Closed Form for Centered Hexagonal Numbers:
 * $H_n = 3 n \paren {n - 1} + 1$

Hence: