The dipole (hyper)polarizability of the copper dimer has been obtained from conventional ab initio and density functional theory calculations. A very large (23s16p12d6f) basis set consisting of 346 Gaussian-type functions is thought to provide reference results of near-Hartree-Fock quality for all properties. We obtain (α) over bar = 102.54 and Deltaalpha = 41.89 for the mean and the anisotropy of the dipole polarizability (alpha(alphabeta)/e(2)a(0)(2)E(h)(-1)). For the Cartesian components and the mean of the hyperpolarizability (10(-3)gamma(alphabetagammadelta)/e(4)a(0)(4)E(h)(-3)) we obtain gamma(zzzz) = 309, gamma(xxxx) = 209, gamma(xxzz) = 87, and (γ) over bar = 244. Electron correlation lowers (α) over bar but increases considerably Deltaalpha. The effect on the hyperpolarizability is enormous, as the longitudinal component y(zzzz) is drastically reduced, while and gamma(xxzz) are nearly halved. At the CCSD(T) level of theory with a [7s6p6d2f] basis set we obtain (α) over bar = 93.82, Deltaalpha = 67.09 and gamma(zzzz) = 18, gamma(xxxx) = 101, gamma(xxzz) = 35, and (γ) over bar = 86. The dipole polarizability varies as [(α) over bar (R) - (α) over bar (R-e)]/e(2)a(0)(2)E(h)(-1) = 28.09(R - R-e) + 4.69(R - R-e)(2) - 0.52(R - R-e)(3) - 0.36(R - R-e)(4) and [Deltaalpha(R) - Deltaalpha - (R-e)]/e(2)a(0)(2)E(h)(-1) = 49.58(R - R-e) + 11.92(R - R-e)(2) - 1.94(R - R-e)(3) - 1.32(R - R-e)(4) around the experimental bond length R-e = 2.2197 Angstrom. B3LYP density functional theory calculations with a [8s7p7d5f] basis set yield (α) over bar = 77.62, Deltaalpha = 44.73e(2)a(0)(2) E-h(-1), and (γ) over bar = (95.9 x 10(3))e(4)a(0)(4)E(h)(-3). These values differ from the conventional ab initio results. The present investigation shows that the longitudinal component and the mean of the hyperpolarizability are positive around Re, in conflict with previous findings. The extension of (hyper)polarizability calculations to higher copper clusters is highly nontrivial and will require the development of new computational strategies.