Inelastic neutron scattering in variable magnetic field and high-field magnetization measurements, at the milikelvin temperature range, were performed to gain insight into the low-energy magnetic excitation spectrum and the field-induced level crossings in the molecular spin cluster {Cr$_8$}-cubane. These complementary techniques provide consistent estimates of the lowest level-crossing field. The overall features of the experimental data are explained using an isotropic Heisenberg model, based on three distinct exchange interactions linking the eight Cr$^{text{III}}$ paramagnetic centers (spins $s = 3/2$), that is supplemented with a relatively large molecular magnetic anisotropy term for the lowest S=1 multiplet. It is noted that the existence of the anisotropy is clearly evident from the magnetic field dependence of the excitations in the INS measurements, while the magnetization measurements are not sensitive to its effects.
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