The Cu substrates have the advantages of no ferromagnetic contribution to hysteretic AC losses, and low cost compared to Ni substrates. We investigated the Jc - B properties of YBCO films deposited on the cube-textured Cu tapes with intervening buffer layers. A protective Ni overlayer was added on top of the cube-textured Cu tape by electroplating to reduce the oxidation rate of the Cu substrate. The YBCO films prepared on the CeO2/YSZ/CeO2 buffered Ni-electroplated Cu tapes revealed the transport J(c) exceeding 3.6 MA/cm(2) at 77 K in a self-field. We also confirmed that our Ni-electroplated Cu tape lost its ferromagnetism after 700 degrees C x 1 hour heat treatment.