A sequence not found in the OEIS: part 1

Sequence name: number of way(s) in which a(n) in A066890 can be expressed as the sum(s) of three positive cubes.

1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 3, 2, 2

Examples: a(0) = 1, because 216 = 3^3 + 4^3 + 5^3. a(1) = 1, because 729 = 1^3 + 6^3 + 8^3. a(2) = 1, because 1728 = 6^3 + 8^3 + 10^3. a(3) = 2, because 5832 = 2^3 + 12^3 + 16^3 = 9^3 + 12^3 + 15^3….

I welcome more terms.

PS

Please look forward to part n (n=2,3,4,…).

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