A025381 Numbers that are the sum of 4 distinct nonzero squares in exactly 6 ways.

174, 234, 254, 258, 266, 273, 279, 285, 291, 309, 327, 333, 339, 359, 362, 365, 371, 380, 391, 395, 396, 403, 413, 443, 444, 449, 451, 476, 487, 492, 521, 572, 596, 604, 643, 668, 692, 696, 772, 796, 936, 1016, 1032, 1064, 1448, 1520, 1584, 1776, 1904, 1968, 2288