Triangular Numbers which are Sum of Two Cubes

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Theorem

$28$ is the smallest triangular number which is the sum of $2$ cubes:

\(\displaystyle 28\) \(=\) \(\displaystyle 1 + 27\)
\(\displaystyle \) \(=\) \(\displaystyle 1^3 + 3^3\)



Proof

Can be demonstrated by brute force.


Sources