Cu2O has been deposited on m-, r-, and a-Al2O3 by reactive sputtering of Cu using Ar with different contents of O2 followed by annealing under carefully optimized conditions at 500 °C under Ar:H2 in order to prevent the oxidation and reduction of the Cu2O layers, which have a cubic crystal structure and are bulk-relaxed. We find that the content of O2 influences the structural and optical properties of the Cu2O layers that exhibited a detailed spectral structure and distinct peaks at 2.75, 2.54, and 2.17 eV corresponding to the indigo, blue, and yellow direct gap transitions of Cu2O as observed by ultrafast pump–probe spectroscopy at room temperature. However, we also observed a transition at 1.8 eV that is related to the occurrence of states ∼0.4 eV below the conduction band minimum of Cu2O. We discuss the controversial origin of these states, which are usually attributed to donor-like oxygen vacancy states, and suggest that the origin of these states may be related to traps at the interfaces of CuO/Cu2O nanostructures, which is important in the context of energy conversion pertaining to solar cells and photocatalysis.