We report a systematic investigation of the magnetic properties including the exchange bias (EB) effect in an iron oxide nanocube system with tunable phase and average size (10, 15, 24, 34, and 43 nm). X-ray diffraction and Raman spectroscopy reveal the presence of Fe3O4, FeO, and α-Fe2O3 phases in the nanocubes, in which the volume fraction of each phase varies depending upon particle size. While the Fe3O4 phase is dominant in all and tends to grow with increasing particle size, the FeO phase appears to coexist with the Fe3O4 phase in 10, 15, and 24 nm nanocubes but disappears in 34 and 43 nm nanocubes. The nanocubes exposed to air resulted in an α-Fe2O3 oxidized surface layer whose thickness scaled with particle size resulting in a shell made of α-Fe2O3 phase and a core containing Fe3O4 or a mixture of both Fe3O4 and FeO phases. Magnetometry indicates that the nanocubes undergo Morin (of the α-Fe2O3 phase) and Verwey (of the Fe3O4 phase) transitions at ~250 K and ~120 K, respectively. For smaller nanocubes (10, 15, and 24 nm), the exchange bias (EB) effect is observed below 200 K, of which the 15 nm nanocubes showed the most prominent EB with optimal antiferromagnetic (AFM) FeO phase. No EB is reported for larger nanocubes (34 and 43 nm). The observed EB effect is ascribed to the strong interfacial coupling between the ferrimagnetic (FiM) Fe3O4 phase and AFM FeO phase, while its absence is related to the disappearance of the FeO phase. The Fe3O4/ α-Fe2O3 (FiM/AFM) interfaces are found to have negligible influence on the EB. Our findings shed light on the complexity of the EB effect in mixed-phase iron oxide nanosystems and pave the way to design exchange-coupled nanomaterials with desirable magnetic properties for biomedical and spintronic applications.