Cobalt oxides have been modified with Cu using different methods to obtain the catalysts of Cu-ZIF-400 (copper-doped cobalt oxide), CuO/Co₃O₄ and Co₃O₄ with identical morphology of hollow polyhedral nanocages. These catalysts were investigated simultaneously for electrocatalytic and photocatalytic water oxidation for the first time. Among them, Cu-ZIF-400 can act as the best electrochemical water oxidation catalyst with a low oxygen evolution reaction (OER) overpotential of 342 mV at 10.0 mA cm^-2 in alkaline electrolyte. At the same time, a high turnover frequency (TOF) of 2.1 x 10^-3 s^-1 per metal atom was obtained over Cu-ZIF-400 at neutral conditions, which is comparable to those documented cobalt based catalysts. The different performances of catalysts can be attributed to the different doping methods. We hypothesize that the electrophilic Cu²⁺ makes the Co more electron-drawing and facilitates the nucleophilic addition of water, which enhanced OER activity of Cu-ZIF-400 catalyst.