We show that in cubic crystals with anisotropic impurity centers the sum of squares of the magnetic resonance [electron paramagnetic resonance (EPR)] frequencies is invariant with respect to the magnetic field direction. The connection between such an invariant and the g-tensor components of the impurity is derived for different types of centers. The established regularity is confirmed experimentally for the spin-noise spectra of a cubic CaF2−Nd3+ crystal. We show how this property of the EPR spectra can be efficiently used for the assignment of paramagnetic centers in cubic crystals.