The superconductivity recently found in the doped topological insulator Cu(x)Bi₂Se₃ offers a great opportunity to search for a topological superconductor. We have successfully prepared a single-crystal sample with a large shielding fraction and measured the specific-heat anomaly associated with the superconductivity. The temperature dependence of the specific heat suggests a fully gapped, strong-coupling superconducting state, but the BCS theory is not in full agreement with the data, which hints at a possible unconventional pairing in Cu(x)Bi₂Se₃. Also, the evaluated effective mass of 2.6m(e) (m(e) is the free electron mass) points to a large mass enhancement in this material.