Compared to isolated C₆₀³⁻ ions, characterized by a three-dimensional equipotential trough at the bottom of the lowest adiabatic potential energy surface (APES), the Jahn-Teller (JT) effect in cubic fullerides is additionally influenced by the interaction of JT distortions at C₆₀ sites with vibrational modes of the lattice. This leads to modification of JT stabilization energy and to the warping of the trough at each fullerene site, as well as to the interaction of JT distortions at different sites. Here we investigate these effects in three fcc fullerides with A = K, Rb, Cs and in Cs₃C₆₀ with bcc (A15) structure. DFT calculations of orbital vibronic coupling constants at C₆₀ sites and of phonon spectra have been done for fully ordered lattices (1 C₆₀/u.c.). Based on them the elastic response function for local JT distortions has been evaluated and the lowest APES investigated. To this end an expression for the latter as a function of trough coordinates of all sites has been derived. The results show that the JT stabilization energy slightly increases compared to an isolated C₆₀³⁻ and a warping of the trough of a few meV occurs. The interaction of JT distortions on nearest- and next-nearest-neighbor fullerene sites is of similar order of magnitude. These effects arise first of all due to the interaction of C₆₀ sites with the displacements of neighbor alkali atoms and are more pronounced in fcc fullerides than in the A15 compound. The results of this study support the picture of weakly hindered independent rotations of JT deformations at C₆₀ sites in cubic A₃C₆₀.