First number having n representations as the sum of up to 9 cubes.
1, 8, 35, 72, 133, 189, 216, 224, 280, 376, 411, 496, 533, 472, 568, 624, 712, 720, 784, 783, 908, 946, 992, 945, 1062, 1072, 1081, 1107, 1153, 1161, 1224, 1288, 1376, 1377, 1449, 1459, 1547, 1496, 1504, 1593, 1592, 1712, 1719, 1648, 1783, 1800, 1837, 1864
1
Nine cubes are always enough. Note that A025453(s(n)) = n.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Eric W. Weisstein, MathWorld: Partition
(Mma) mx = 10; t = Table[0, {mx^3}]; Do[n = a^3 + b^3 + c^3 + d^3 + e^3 + f^3 + g^3 + h^3 + i^3; If[0 < n <= mx^3, t[[n]]++], {a, 0, mx}, {b, 0, a}, {c, 0, b}, {d, 0, c}, {e, 0, d}, {f, 0, e}, {g, 0, f}, {h, 0, g}, {i, 0, h}]; last = Complement[Range[Max[t]], Union[t]][[1]] - 1; Table[Position[t, n, 1, 1][[1, 1]], {n, last}]
Cf. A025453, S000611, S000612.
nonn
T. D. Noe, Apr 29 2015