A study of the electronic structure of the complete valence shell of cubane is reported. Results from our many-body Green's function calculation, to the third-order algebraic diagrammatic construction (ADC(3)) level, for the binding energies and spectroscopic factors of the respective valence orbitals of cubane are presented. Binding-energy spectra were measured in the energy regime 6-35 eV over a range of different target electron momenta, so that momentum distributions (MDs) could be determined for each orbital. The corresponding theoretical MDs were calculated using a plane wave impulse approximation (PWIA) model for the reaction mechanism and density functional theory (DFT) for the wave function. Seven basis sets, at the local density approximation (LDA) level and, additionally, incorporating nonlocal correlation functional corrections, were studied. The sensitivity of the level of agreement between the experimental and theoretical MDs to the nonlocal corrections is considered. A critical comparison between the experimental and theoretical MDs allows us to determine the 'optimum' wave function for cubane from the basis sets we studied. This wave function is then used to derive cubane's chemically interesting molecular properties. A summary of these results and a comparison of them with those of other workers is presented with the level of agreement typically being good.