We report the results of our degenerate four-wave-mixing measurements (DFWM) on the fullerene series from C-60 to C-96 dissolved in CS2. The DFWM measurements were carried out using 70 ps laser pulses at the wavelength of 0.532 mu m under the optimized experimental conditions. The second hyperpolarizabilities gamma(1111) of all these fullerenes were determined to be on the order of 10(-31)-10(-30) esu, and overall they increase smoothly with the carbon cage size except for C-70 and C-78, which show anomalously larger gamma(1111) values than those of their neighboring cage sizes we investigated. The number of pi-conjugated electrons, geometrical structure, and resonance enhancement are discussed as possible factors responsible for the observed third-order optical nonlinearities of the fullerenes.