For the three-dimensional cubic model, the nonlinear susceptibilities of the fourth, sixth, and eighth orders are analyzed and the parameters (formula presented) characterizing their reduced anisotropy are evaluated at the cubic fixed point. In the course of this study, the renormalized sextic coupling constants entering the small-field equation of state are calculated in the four-loop approximation and the universal values of these couplings are estimated by means of the Padé-Borel-Leroy resummation of the series obtained. The anisotropy parameters are found to be (formula presented) (formula presented) and (formula presented) indicating that the anisotropic (cubic) critical behavior predicted by the advanced higher-order renormalization-group analysis should be, in principle, visible in physical and computer experiments.