The electronic band structure and electronic density of states of cubic SiC nanowires (SiCNWs) in the directions [001], [111], and [112] were studied by means of Density Functional Theory (DFT) based on the generalized gradient approximation and the supercell technique. The surface dangling bonds were passivated using hydrogen (H) atoms and OH radicals in order to study the effects of this passivation on the electronic states of the SiCNWs. The calculations show a clear dependence of the electronic properties of the SiCNWs on the quantum confinement, orientation, and chemical passivation of the surface. In general, surface passivation with either H or OH radicals removes the dangling bond states from the band gap, and OH saturation appears to produce a smaller band gap than H passivation. An analysis of the atom-resolved density of states showed that there is substantial charge transfer between the Si and O atoms in the OH-terminated case, which reduces the band gap compared to the H-terminated case, in which charge transfer mainly occurs between the Si and C atoms.