Superconducting bulks, acting as high-field permanent magnets, are promising for many applications. An important effect in bulk permanent magnets is crossed-field demagnetization, which can reduce the magnetic field in superconductors due to relatively small transverse fields. Crossed-field demagnetization has not been studied in sample shapes such as rectangular prisms or cubes. This contribution presents a study based on both three-dimensional (3-D) numerical modeling and experiments. We study a cubic Gd-Ba-Cu-O bulk superconductor sample of size 6 mm magnetized by field cooling in an external field of around 1.3 T, which is later submitted to crossed-field magnetic fields of up to 164 mT. Modeling results agree with experiments, except at transverse fields 50% or above of the initial trapped field. The current paths present a strong 3-D nature. For instance, at the midplane perpendicular to the initial magnetizing field, the current density in this direction changes smoothly from the critical magnitude, Jc, at the lateral sides to zero at a certain penetration depth. This indicates a rotation of the current density with magnitude Jc, and hence force free effects like flux cutting are expected to play a significant role.