Numerical simulations of the response flow in a fluid-filled rotating cube that is subjected to precessional forcing are examined over a wide range of rotation, precession and forcing frequencies. The responses are shown to correspond to resonantly excited inertial modes of the rotating cube that have the same spatio-temporal symmetry as the precessional forcing and, under certain conditions, the response flow loses stability via symmetry breaking that is intricately associated with a triadic resonance between the forced flow and two free inertial modes whose spatio-temporal symmetries do not coincide with that of the precessional forcing.