Inverse bicontinuous cubic (IBC) structures consisting of triply periodic minimal surfaces of block copolymers (BCPs) are emerging as materials of interest owing to their structural characteristics, which resemble those of their biological counterparts constructed from lipids. Solution self-assembly of amphiphilic BCPs with nonlinear architectures has recently been shown to form colloidal particles (polymer cubosomes) and macroscopic monoliths having mesoporous networks of water channels embedded in the periodic minimal surfaces of the BCP bilayers. Here we report that BCP architectures play a crucial role in controlling the packing parameter (P) of BCPs; a value greater than unity is a prerequisite for preferential self-assembly into IBC mesophases in solution. We show that the branched architecture of the polymer blocks constituting the BCP critically influences the structural parameters, such as the molecular area and, in particular, the critical length of the hydrophobic domain. Adjusting these structural parameters not only increases the P value of the BCP without depending on the asymmetry of the volume ratio of two polymer blocks (block ratio) but also dictates the lattice and periodicity of the resulting minimal surfaces of the BCPs. Our results could provide a rationale to design and synthesize amphiphilic block copolymers to directly self-assemble into periodic porous structures in solution, which could be promising materials having highly ordered mesopore networks.