A numerical study of the 2D Hubbard model at various fillings has been performed. The static properties of 10, 14 and 16 electrons on a 4×4 cluster have been studied by exact diagonalization at intermediate couplings. A simple “power method” has been used in order to minimize memory requirements. Spin-spin, charge-charge and hole-hole correlations have been computed together with the one particle density matrix. This computation provides the first exact results on such a system, which can be used as a test for existing simulation algorithms.