The electrical generation of orbital angular momentum in materials has attracted significant attention due to its fundamental importance and technological potential. Notably, recent experiments on orbital torque and terahertz emission suggest that Cu enables substantial charge-to-orbital interconversion upon oxidation. However, direct evidence of orbital generation in Cu remains elusive. In this work, we demonstrate current-induced orbital accumulation in pristine and naturally oxidized Cu films using magneto-optical Kerr effect measurements. We observe distinct thickness dependences of the Kerr signals in pristine and oxidized films, revealing bulk- and interface-driven orbital generation mechanisms corresponding to the orbital Hall effect and orbital Rashba-Edelstein effect, respectively. The extracted orbital diffusion length in Cu is significantly shorter than its known spin diffusion length, yet still exceeds atomic scales. These findings provide clear evidence of orbital generation in Cu and highlight the distinct bulk and interfacial mechanisms underlying it.