The recent observation of dipole-allowed P excitons up to principal quantum numbers of n=25 in cuprous oxide has given insight into exciton states with unprecedented spectral resolution. While so far the exciton description as a hydrogenlike complex has been fully adequate for cubic crystals, we demonstrate here distinct deviations: The breaking of rotational symmetry leads to mixing of high angular momentum F and H excitons with the P excitons so that they can be observed in absorption. The F excitons show a threefold splitting that depends systematically on n, in agreement with theoretical considerations. From detailed comparison of experiment and theory we determine the cubic anisotropy parameter of the Cu2O valence band.