In this paper, we prove that the Hasse principle for any system of rational cubic forms, any system of rational homogeneous forms of degree at least 3 in an arbitrary number of variables is equivalent to the Hasse principle of certain systems of rational quadratic forms. This shows, in particular, the Hasse principle for any system of rational cubic forms or rational homogeneous forms of degree at least 3 in an arbitrary number of variables holds if and only if the intersection of the nonempty sets of nontrivial rational solutions of each quadratic form of the associated system of quadratic forms is nonempty.

Diophantine equation, quadratic form, cubic form, higher degree form, Hasse principle, local-global principle, systems of forms, solutions of systems of forms.