On the representation of an even perfect number as the sum of a limited number of cubes

TL;DR

This paper proves that all even perfect numbers except 6 can be expressed as the sum of five cubes of natural numbers and conjectures they can be expressed as the sum of three cubes.

Contribution

It establishes a new representation for even perfect numbers as sums of five cubes and proposes a conjecture reducing this to three cubes.

Findings

All even perfect numbers except 6 are sums of five cubes.

Conjecture that these numbers can be expressed as sums of three cubes.

Provides a new perspective on the structure of perfect numbers.

Abstract

The aim of this note is to show that any even perfect number, other than $6$, can be written as the sum of 5 cubes of natural numbers. We also conjecture that any even perfect number, other than $6$, can be written as the sum of only 3 cubes of natural numbers.