Cube Number as Sum of Three Consecutive Odd Squares

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Theorem

$1331 = 11^3 = 19^2 + 21^2 + 23^2$


Proof

\(\displaystyle 19^2 + 21^2 + 23^2\) \(=\) \(\displaystyle 361 + 441 + 529\)
\(\displaystyle \) \(=\) \(\displaystyle 1331\)

$\blacksquare$


Historical Note

In his Curious and Interesting Numbers, 2nd ed. of $1997$, David Wells attributes this result to Michal Stajsczak, but gives no context.


Sources