A025389 Numbers that are the sum of 4 distinct nonzero squares in 5 or more ways.

126, 150, 170, 174, 186, 190, 198, 210, 219, 222, 225, 230, 231, 234, 238, 242, 246, 249, 250, 254, 255, 258, 261, 266, 267, 270, 273, 274, 275, 278, 279, 282, 285, 286, 287, 290, 291, 294, 295, 297, 302, 303, 305, 306, 309, 310, 311, 314, 315, 318, 319, 321, 322, 323