Perfect Number is Sum of Successive Odd Cubes except 6/Mistake

Source Work

 * The Dictionary
 * $6$
 * $6$


 * The Dictionary
 * $6$
 * $6$

Mistake

 * [ 6|$6$ ] is the only perfect number that is not the sum of successive cubes.

Correction
The statement should be:
 * [ 6|$6$ ] is the only even perfect number that is not the sum of successive odd cubes.

For example:


 * $496 = 1 + 27 + 125 + 343 = 1^3 + 3^3 + 5^3 + 7^3$

It is appreciated that it is not known whether there exist any odd perfect numbers.

However, for complete accuracy it is necessary to include a qualification of the parity of the perfect numbers for which the statement does in fact hold.