We will show that if d is a cubefree integer and n is an integer, then with some suitable conditions, there are no primes p and a positive integer m such that d is a cubic residue (mod p), $3;{ mid};m$, p || n if and only if there are integers x, y, z such that $$x^3;+;dy^3;+;d^2z^3;-;3dxyz;=;n$$.