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The effect of changes in the damping rate of cavity side modes on the noise fluxes of a three-mode class-A laser is analytically investigated using the fluctuation-dissipation theorem. The Maxwell-Bloch equations of motion are first solved in the presence of three cavity Langevin forces associated with the simultaneous oscillation of cavity central mode as well as its left and right adjacent modes. The solutions are then used to determine the fluctuations that imposed by the cavity Langevin forces on the phase and amplitude of oscillating components of cavity electric field, and on the static and dynamic components of atomic population inversion. By taking the correlation function of these fluctuating components, the noise fluxes of laser and spontaneous emission will be specified in frequency domain. On the other hand, the noise flux of pumping is differently determined by taking the correlation function of fluctuation conservation relation. The results indicate that the cavity Langevin force of each of three oscillating modes makes a direct contribution in producing the noise fluxes of other two oscillating modes. Finally, it is demonstrated that the noise fluxes of input pumping and output laser and spontaneous emission satisfy the flux (energy) conservation.