We construct thermodynamic potentials for two superionic phases of water [with body-centered cubic (bcc) and face-centered cubic (fcc) oxygen lattice] using a combination of density functional theory (DFT) and molecular dynamics simulations (MD). For this purpose, a generic expression for the free energy of warm dense matter is developed and parametrized with equation of state data from the DFT-MD simulations. A second central aspect is the accurate determination of the entropy, which is done using an approximate two-phase method based on the frequency spectra of the nuclear motion. The boundary between the bcc superionic phase and the ices VII and X calculated with thermodynamic potentials from DFT-MD is consistent with that directly derived from the simulations. Differences in the physical properties of the bcc and fcc superionic phases and their impact on interior modeling of water-rich giant planets are discussed.