Cubic Al _x Ga_1-x N/GaN heterostructures were grown by plasma-assisted molecular beam epitaxy on free-standing 3C-SiC(001). The samples consist of an unintentionally doped 600 nm thick c-GaN buffer and a 30 nm c-Al_0.3Ga_0.7N layer. Capacitance–voltage measurements were performed on metal–oxide–semiconductor heterojunction structure using SiO₂ as an insulator. A depth profile of the net donor concentration N _CV of the grown sample was measured, demonstrating a clear carrier accumulation at the heterojunction. By electron holography in a transmission electron microscope the potential profile was measured and a free electron concentration of 5.1×10¹¹ cm^-2 was estimated at the c-Al _x Ga_1-x N/GaN interface. Using a one-dimensional (1D) Poisson simulator the results of both techniques are compared and a conduction-to-valence band offset ratio of about 4:1 for the cubic Al _x Ga_1-x N/GaN interface is estimated, which promotes the electron accumulation. Our results demonstrate that the two-dimensional electron gas (2DEG) in cubic Al _x Ga_1-x N/GaN heterostructures can be achieved without the need of polarization effects and is due to the residual background doping in the Al _x Ga_1-x N and GaN.