63 is a centered octahedral number. That means if you
build an approximation of an octahedron with cubes, one size of octahedron will
have 63 cubes.In the late 1700’s René Just Haüy developed a theory
about how crystals formed: successive layers of fundamental primitives in
orderly arrangements. One of those arrangements was stacking cubes together to
make an octahedron.Start with one cube:Add six more cubes around it, one on each face. Now we have seven:Add another layer, adding a cube to touch each visible cube, making 25:One more layer and we have a total of 63:The remaining numbers in the sequence
less than 10,000 are 129, 231, 377, 575, 833, 1159, 1561, 2047, 2625, 3303,
4089, 4991, 60…