The presently unknown band offset in nonpolar cubic GaN/AlN superlattices is investigated by inter-sub-band and interband spectroscopies as well as ab initio calculations. On one hand, the conduction-band offset (CBO) has been determined from the comparison of the measured transition energies with model calculations within the effective mass approximation. On the other hand, the valence-band offset (VBO) and the CBO are accurately simulated by calculating many-body corrections within the GW approximation on top of hybrid-functional density functional theory calculations. Thus, a CBO of (1.4 ± 0.1) eV and a VBO of (0.5 ± 0.1) eV is obtained as a result of both approaches.