A025409 Numbers that are the sum of 4 distinct positive cubes in exactly 2 ways.

1036, 1134, 1352, 1367, 1430, 1465, 1484, 1547, 1582, 1638, 1709, 1736, 1764, 1800, 1801, 1820, 1862, 1863, 1881, 1918, 1953, 1972, 2009, 2070, 2080, 2099, 2136, 2197, 2268, 2288, 2305, 2331, 2340, 2422, 2464, 2483, 2485, 2520, 2548, 2584, 2799, 2800