Triangular Numbers which are Sum of Two Cubes

Theorem
The sequence of triangular numbers which are the sum of $2$ cubes is:


 * $28, 91, 351, 2926, 8001, 46971, 58653, 93528, 97461$

Proof
Can be demonstrated by brute force.

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