The nonlinear characteristics of the electro-optic components are the major limiting factor to realize a multilevel signal transmission. Cascaded multi-modulus algorithm (CMMA) is a popular blind equalization scheme that can compensate for only linear distortions without using any training sequence. In this paper, a modified CMMA is proposed to blindly adapt the tap weights of a receiver-side nonlinear Volterra equalizer (NLVE) to mitigate both linear and nonlinear distortions. Furthermore, a nonlinear sparse Volterra equalizer (NLSVE) is suggested in this paper that can achieve similar performance with a substantial reduction of complexity, in comparison with an NLVE. Experimental results for a 25 Gb/s PAM-4 transmission in the 1310-nm band over a 20-km single-mode fiber (SMF-28e) using a commercial 10 GHz-class directly modulated laser (DML) for an intensity modulation direct-detection (IM/DD) optical access network verify that the proposed NLSVE can achieve a gain of similar to 2-dB in comparison with a traditional CMMA.