A038597 Numbers n such that n^2 is a difference between 2 positive cubes in at least one way.

13, 28, 49, 104, 147, 181, 189, 224, 351, 361, 388, 392, 507, 549, 588, 676, 756, 832, 1029, 1176, 1323, 1369, 1425, 1448, 1512, 1625, 1792, 1862, 1911, 1922, 2299, 2355, 2521, 2808, 2883, 2888, 3104, 3136, 3185, 3216, 3500, 3721, 3969, 4056, 4103, 4332