We report here surface x-ray scattering studies of the adsorption of simple hydrocarbon liquid films on nanostructured surfaces-silicon patterned by an array of nanocavities. Two different regimes, filling and growing, are observed for the wetting film evolution as a function of the chemical potential offset from the bulk liquid-vapor coexistence. The strong influence of geometrical effects is manifested by a dependence of liquid adsorption in the nanocavities that is stronger than the van der Waals behavior for flat surfaces. The observed dependence is, however, much weaker than predicted for the infinitely deep parabolic cavities, suggesting that the finite-size effects contribute significantly to the observed adsorption behavior.