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The magnetic relaxation of single-domain ferromagnetic particles with cubic magnetic anisotropy is treated by averaging the Gilbert-Langevin equation for an individual particle, so that the system of linear differential-recurrence relations for the appropriate equilibrium correlation functions is derived without recourse to the Fokker-Planck equation. The solution of this system (in terms of matrix continued fractions) is determined and the longitudinal relaxation time and spectrum of the complex magnetic susceptibility are evaluated. It is shown that in contrast to particles with uniaxial anisotropy, there is an inherent geometric dependence of the complex susceptibility and the relaxation time on the damping parameter arising from coupling of longitudinal and transverse relaxation modes.