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

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Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary
$6$


1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary
$6$


Mistake

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


Correction

The statement should be:

[ $6$ ] 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.


Sources