The effects on the electronic band structure of hydrogenated cubic silicon carbide ($\beta$-SiC) nanowires of changes in the diameter and morphology are studied using a semiempirical sp3s* tight-binding approach applied to a supercell model. The results of the calculation of the electronic band structure and electronic density of states obtained are compared with those calculated by density functional theory within local density approximation only for the bulk of $\beta$-SiC. As boundary conditions, we passivated all the Si and C dangling bonds with hydrogen atoms. The results show that although surface morphology modifies the band gap, the change is more systematic with the thickness variation. The energy band gap increases with decreasing diameter in all cases because of quantum confinement, but the scaling is dependent on the morphology (cross-section) of the $\beta$-SiC nanowires. Finally, the calculations show a consistent asymptotical behavior to the crystalline limit when the width of the wires enlarges. {\textcopyright} (2009) Trans Tech Publications, Switzerland.