The adsorption of several quadrupolar and nonpolar gases on the Metal Organic Framework Cu-BTC has been studied by combining experimental measurements and Monte Carlo simulations. Four main adsorption sites for this structure have been identified: site I close to the copper atoms, site I′ in the bigger cavities, site II located in the small octahedral cages, and site III at the windows of the four open faces of the octahedral cage. Our simulations identify the octahedral cages (sites II and III) and the big cages (site I′) as the preferred positions for adsorption, while site I, near the copper atoms, remains empty over the entire range of pressures analyzed due to its reduced accessibility. The occupation of the different sites for ethane and propane in Cu-BTC proceeds similarly as for methane, and shows small differences for O2 and N2 that can be attributed to the quadrupole moment of these molecules. Site II is filled predominantly for methane (the nonpolar molecule), whereas for N2, the occupation of II and I′ can be considered almost equivalent. The molecular sitting for O2 shows an intermediate behavior between those observed for methane and for N2. The differences between simulated and experimental data at elevated temperatures for propane are tentatively attributed to a reversible change in the lattice parameters of Cu-BTC by dehydration and by temperature, blocking the accessibility to site III and reducing that to site I′. Adsorption parameters of the investigated molecules have been determined from the simulations.