Polymer cubosomes (PCs) are a recent class of self-assembled block copolymer (BCP) microparticles with an accessible periodic channel system. Most reported PCs consist of a polystyrene scaffold, which provides mechanical stability for templating but has a limited intrinsic functionality. Here, we report the synthesis of photocleavable BCPs with compositions suitable for PC formation. We analyze the self-assembly mechanism and study the model release of dyes during irradiation, where the transition of the BCPs from amphiphilic to bishydrophilic causes the rapid disassembly of the PCs. A combination of modeling and experiment shows that the evolution of PCs proceeds first via liquid-liquid phase separation into polymer-rich droplets, followed by microphase separation within this droplet confinement, and finally, membrane reorganization into high internal order. This insight may encourage exploration of alternative preparation strategies to better control the size and homogeneity of PCs.