A038595 Numbers n such that n and n-1 are differences between 2 positive cubes in at least one way.

218, 387, 2169, 2170, 2402, 2717, 3088, 3753, 6517, 7352, 9424, 9577, 10108, 12097, 13085, 13481, 14770, 14833, 18487, 20313, 29764, 32465, 32761, 36632, 37297, 37449, 39816, 50311, 54406, 58330, 58808, 63657, 67545, 78345, 81712, 83286