We calculate ground-state energies and density distributions of Hubbard superlattices characterized by periodic modulations of the on-site interaction and the on-site potential. Both density-matrix renormalization group and density-functional methods are employed and compared. We find that small variations in the on-site potential v i can simulate, cancel, or even overcompensate effects due to much larger variations in the on-site interaction U i . Our findings highlight the importance of nanoscale spatial inhomogeneity in strongly correlated systems, and call for a reexamination of model calculations assuming spatial homogeneity. A large part of the complexity of strongly correlated systems arises from the multiple phases that coexist or compete in their phase diagrams. Metallic and insulating phases are separated by metal-insulator transitions, and subject to the formation of various types of long-range order, such as antiferromagnetism, superconductivity, and charge-or spindensity waves. The relative stability of such phases is determined by differences in appropriate thermodynamic potentials, or, at zero temperature, in their ground-state energies. Identification of the appropriate order parameters and calculation of the ground-state energies of the various phases is a complicated problem, and the nature of the phase diagram of many strongly correlated systems is still subject to considerable controversy. It is widely believed, however, that a minimal model containing the essence of strong correlations, and displaying many of the above-mentioned phases, is the homogeneous Hubbard model, which in one dimension and standard notation readsMuch theoretical effort is thus going into the analysis of the homogeneous Hubbard model and the clarification of the nature of its ground state. In a parallel development, nanoscale spatial inhomogeneity has been observed experimentally to be a ubiquitious feature of strongly correlated systems, 1-8 but although its importance is widely recognized, the consequences of such inhomogeneity are still insufficiently understood. The present paper investigates the effects of, and the competition between, two different manifestations of nanoscale inhomogeneity in strongly correlated systems, namely local variations in the on-site potential and in the on-site interaction. We base our analysis on the inhomogeneous Hubbard model