Using a perturbation theory with a hard-sphere reference system we have directly calculated free energies of fluid and solid phases of aluminum with an embedded atom model potential. Unlike other approaches such as thermodynamic integration, we do not require any simulations. Moreover, the free energies of the two different phases are calculated in a single approach, unlike approximations like the quasi-harmonic solid approach. The calculated free energies are with an average relative error 0.55% of the simulation values and the resulting melting temperature is within 5% of the simulation value.