Ternary surfactant cubic phases exhibit a sharp melting transition. We investigate the effect of concentration fluctuations in this system which are a possible driving mechanism for the phase transition. We consider local variations in the surfactant concentration and impose the conditions of a fixed topology, volume, and surface area of surfactant. The energy is derived from changes in curvature and is given by the Helfrich Hamiltonian in contrast to a naive expectation from dilation invariance. We find that the constraints give rise to an energy change which contributes to the bulk modulus and gives the expected (V delta phi(r))(2) term. The decay of the fluctuations is also examined, and a relaxation time that contains both diffusive and soft modes is obtained. We compare estimated times with experimental values which we have measured by performing dynamic light scattering on cubic phases of didodecyl-dimethylammoniumbromide/toluene/H2O. In the range of wave vectors studied we observe only the diffusive modes; these times are predicted by the theory. In addition we consider the consequences of fluctuations to theological measurements. We present theological results that clearly show the melting transition.