Cluster calculation of carbon and silicon vacancies in cubic SiC has been performed for the charge states of +1, 0 and -1 and possible spin states. The density functional theory has been used with the B3LYP exchange-correlation functional and Gaussian basis set applied to the 52- and 70-atom clusters. Being suitable for a comparison with EPR data, the calculations of hyperfine coupling parameters for atoms of the first and second shells of vacancies have been performed. The test calculations have been done to check the validity of applied approximations, and reasonable agreement between calculated and experimental data has been obtained. The ground spin state and the defect point symmetry for all the above-mentioned charge states have been determined along with the hyperfine parameters for atoms of the first and second shells. In the ground state, spins of V-C(-), V-Si(-) and V-Si(+) have the value of S = 3/2 while S = 1 for V-C(0) and V-Si(0), and S = 1/2 for V-C(+). Optimization of geometry leads to a minimum with the Tu symmetry only for V-C(-), V-Si(-) and V-Si(+) centers. At the same time, V-Si(0) and V-C(+) defects have D-2d symmetry, while V-C(0) has C-3V symmetry. All the considered charge states of the carbon vacancy exhibit remarkably stronger hyperfine interaction with the nearest and next-nearest neighbors as compared to the silicon vacancy.