Rayleigh and Brillouin scattering measurements have been performed for liquid hexane-methanol mixtures in their one-phase region. The concentration-concentration fluctuation S-cc(0) for this system could be derived from the total scattering intensity and the Brillouin frequency shift with the molar volume and the polarizability data. The obtained S-cc(0) shows a tendency of divergence near the critical temperature. The Gibbs free energy of mixing Delta G was also derived successfully by integrating S-cc(0). A plausible temperature dependence for Delta G has been obtained.