While the theory of quadratic forms is quite well developed (in the last century), the case of cubic forms is far more involved. We show that cubic forms equivalence is as hard as F-algebra isomorphism, which is as hard as graph isomorphism. Also, the 'hardness' of these questions seem to depend on the underlying field F. We will see that for the complex and the finite field F, the problems seem 'easier' than that over the field of rationals.