100^(6p+1) =
= 100 × 100^(6p) =
= (1 + 8 + 27 + 64) × 100^(6p) =
= 1 × 100^(6p) + 8 × 100^(6p) + 27 × 100^(6p) + 64 × 100^(6p) =
= 1^3 × [100^(2p)]^3 + 2^3 × [100^(2p)^3] + 3^3 × [100^(2p)^3] + 4^3 × [100^(2p)^3] =
= [100^(2p)]^3 + [2 × 100^(2p)]^3 + [3 × 100^(2p)]^3 + [4 × 100^(2p)]^3
