[math-fun] Unsolved number theory problem

Which integers S are the sum of three cubes: S = J^3 + K^3 + L^3 ??? (None of the form S == ±4 (mod 9), for instance.) Some low numbers are hard to find the J, K, L for, like: 30 = (−662037799708799)3 + 1908092688412843 + 6567116892545653 . The first S for which a solution is unknown is 33. The complete list of S < 1000 with no known solution (as far as I can tell) is as follows: 33 42 114 165 390 579 627 633 732 795 906 921 975 . —Dan