Self-assembly of block copolymers into colloidal particles with highly ordered porous structures in their interior is an emerging strategy to create mesoporous structures having desired porosity and surface functionality. Polymer cubosomes are colloidal particles consisting of triply periodic minimal surfaces of block copolymer bilayers. The symmetry and dimension of internal lattices of polymer cubosomes can be adjusted by the chemical nature and architecture of block copolymer building blocks. Polymer cubosomes can be interesting porous structures for catalysis, separation, and nanotemplating. In this presentation, we will discuss the structural requirements of block copolymers to create polymer cubosomes with the desired symmetry and dimension of the internal lattice. We also discuss the potential applications of these bicontinuous mesophases of block copolymers having beautiful mazes of nanochannels.