Analogous to the complex lipid membranes found in cellular organelles, such as the endoplasmic reticulum, the inverse cubic mesophases of block copolymers and their colloidal forms (polymer cubosomes) possess internal networks of large water channels arranged in crystalline order, which provide a unique nanospace for biocatalysis and synthesis of hybrid materials. We recently discovered a new self-assembly behavior of block copolymers having bulky branched hydrophilic blocks into triply periodic minimal surfaces in solution. This direct self-assembly of block copolymers into inverse bicontinuous cubic mesophases in solution is an emerging method to create highly regular bicontinuous porous polymers without any aid of post processes to generate internal pore networks and surface functional groups. To establish the design rule of the block copolymers for forming inverse mesophases, we synthesized a series of model block copolymers of varying architectures to investigate the effect of architecture of the block copolymers on their solution self-assembly into inverse mesophases consisting of the block copolymer bilayer. In this presentation, we wish to suggest that the branched architecture of the hydrophilic block is a crucial structural requirement for the preferential self-assembly of the resulting block copolymers into inverse bicontinuous cubic phases.