Conventional self-assembly methods of block copolymers in cosolvents (i.e., usually water and organic solvents) has yet to produce a pure and monodisperse population of nanocubes. The requirement to assemble a nanocube is for the second block to have a high molecular weight. However, such high molecular weight block copolymers usually result in the formation of kinetically trapped nanostructures even with the addition of organic cosolvents. Here, we demonstrate the rapid production of well-defined polymer nanocubes directly in water by utilizing the thermoresponsive nature of the second block (with 263 monomer units), in which the block copolymer was fully water-soluble below its lower critical solution temperature (LCST) and would produce a pure population of nanocubes when heated above this temperature. Incorporating a pH-responsive monomer in the second block allowed us to control the size of the nanocubes in water with pH and the LCST of the block copolymer. We then used the temperature and pH responsiveness to create an adaptive system that changes morphology when using a unique fuel. This fuel (H2O2 + MnO2) is highly exothermic, and the solution pH increases with the consumption of H2O2. Initially, a nonequilibrium spherical nanostructure formed, which transformed over time into nanocubes, and by controlling the exotherm of the reaction, we controlled the time for this transformation. This block copolymer and the water-only method of self-assembly have provided some insights into designing biomimetic systems that can readily adapt to the environmental conditions.