Copper is an earth-abundant element that can be used to reduce the high cost and unsatisfactory durability of pure Pt catalysts by the formation of bimetallic Pt-M nanocrystals. Among CuPt nanostructures, nanocages attract great interest for catalysis as they allow passage of reactant species to their porous interiors, which provide a high fraction of surface sites. They may also enhance reactivity through an increase in collision frequency by enclosing reagents within nanoscale cavities and by lattice strain effects of the alloy. Recent reports apply solvothermal chemistry to obtain CuPt nanocages in one step. However, there is still a lack of understanding in the formation mechanism and its impact on catalytic activity for such hollow CuPt nanostructures. In this work, we adopt a two-step method in which we synthesize rhombic dodecahedral (RD) Cu-CuPt core-shell nanocrystals by the deposition of Pt on Cu nanocubes to form CuPt shells less than 2 nm in thickness, followed by removing Cu cores to obtain ultrathin octahedral (OCT) nanocages for catalytic applications. By adjustment to shorter and longer reaction time frames, the core-shell nanocrystals were also made into quasi-RD (QRD) and spiny-RD (SRD) morphologies, which lead to porous (POCT) and spiny (SOCT) OCT nanocages, respectively, upon etching. These three types of CuPt nanocages (POCT, OCT, and SOCT) were then examined in the electrocatalytic oxygen reduction reaction (ORR) and the hydrogen evolution reaction (HER) by the hydrolysis of NH3BH3 to study their performance. As a result, the SOCT CuPt nanocages exhibit the highest Pt mass activity (0.3 A/mgPt) in the ORR, a 3-fold improvement over commercial Pt/C. They also show the lowest activation energy (24.3 kJ/mol) in the HER that is better than the commercial catalyst by a factor of 4. HER photocatalysis results show that the POCT and OCT nanocages have localized surface plasmon resonance (LSPR)-enhancement while the SOCT nanocages do not, which is attributed to inhomogeneity in Cu-Pt distributions at shorter reaction times.