A038849 Numbers that are divisible by 4 and are differences between two cubes in at least one way.

56, 124, 152, 208, 296, 316, 448, 488, 504, 604, 728, 784, 936, 988, 992, 1016, 1216, 1304, 1352, 1468, 1512, 1664, 1720, 1736, 1744, 2044, 2072, 2168, 2196, 2232, 2368, 2528, 2648, 2680, 2716, 2736, 3032, 3088, 3096, 3176, 3348, 3484, 3584, 3752, 3880