Channel-facilitated transport of metabolites across biological membranes results in excess noise in the current carried by small ions. This noise originates from fluctuations of the number of metabolite molecules in the channel due to their diffusion. We have carried out a theoretical study of particle number fluctuations in a cylindrical pore. First, we obtain the power spectral density of these fluctuations as a function of pore length and radius, as well as the diffusion constants of the particle in the pore and in the bulk, in the absence of particle-pore interactions. We then perform three-dimensional Brownian dynamics simulations that show excellent agreement with the analytical result. Finally, we demonstrate that explicit expressions for the low-frequency limit of the spectral density can be found even when the particle interacts with the pore.