Valence electron contributions to the static molecular third-order polarizabilities (gamma) are calculated for C-60, C-70, and two stable structures of C-84 (D-2 and D-2d). The method utilized is based on the finite-field approach coupled with semiempirical polarization calculations on all-valence electrons. An increase in the third-order polarizability contributions is observed for molecular structures with a reduction in group symmetry, in agreement with recent experimental observations for these fullerenes. This increase is attributed mainly to the appearance of aromatic structures within the molecules as well as to the increase in molecular volume.