Cubes which are Sum of Five Cubes

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Theorem

The following cube numbers can be expressed as the sum of $5$ positive cube numbers:

$9^3, \ldots$




Proof

\(\ds 9^3\) \(=\) \(\ds 729\)
\(\ds \) \(=\) \(\ds 1 + 27 + 64 + 125 + 512\)
\(\ds \) \(=\) \(\ds 1^3 + 3^3 + 4^3 + 5^3 + 8^3\)



Sources