Even Perfect Number is Hexagonal

Theorem
All perfect numbers which are even are hexagonal.

Proof
Let $a$ be an even perfect number.

From the Theorem of Even Perfect Numbers, $a$ is in the form $2^{p - 1} \paren {2^p - 1}$ where $2^p - 1$ is prime.

Thus:

The result follows from Closed Form for Hexagonal Numbers.