We used our recently developed mesoscale amphiphilic lattice-Boltzmann method (Nekovee, M.; Coveney, P.V.; Chen, H.; Boghosian, B.M. Phys. Rev. E 2000, 62, 8282-8894) to investigate the dynamics of self-assembly of the bicontinuous cubic phase in a binary water-surfactant system, and the transition from the lamellar structure to a bicontinuous cubic phase. Our study provides insight into how such structures emerge as a result of competing molecular interactions between water and amphiphiles and among amphiphilic molecules themselves, and represents the first application of any lattice-Boltzmann model to amphiphilic systems in three dimensions.