Numbers represented by a cubic form
Solution 1:
As the OP pointed out, Noam Elkies answered at https://mathoverflow.net/questions/127160/numbers-integrally-represented-by-a-ternary-cubic-form/127295#127295
As the OP pointed out, Noam Elkies answered at https://mathoverflow.net/questions/127160/numbers-integrally-represented-by-a-ternary-cubic-form/127295#127295