The complex dielectric function for cubic InN is determined by spectroscopic ellipsometry from the mid-infrared into the visible spectral region. Films were grown by molecular beam epitaxy on c-GaN/3C-SiC pseudo-substrates. The high electron densities above 1019 cm−3 cause pronounced Burstein–Moss shifts at the gap. Taking into account the non-parabolicity and the filling of the conduction band, data analysis yields renormalized band edges between 0.43 and 0.455 eV. Including carrier-induced band-gap renormalization, we estimate a zero-density band gap of ~0.595 eV for c-InN which is about 85 meV lower than for hexagonal InN. Values for the electron effective mass, the static and high-frequency dielectric constant are reported.