We consider the problem of quantifying the variance in molecular numbers in biochemical reactions with nonlinear reaction rates. We address this problem for a specific configuration where a spontaneously formed species determines the rate of formation of another species via a nonlinear reaction rate, with the aim being to quantify the variance of this species. By making use of an appropriate decomposition based on Newton series expansion we derive an analytical expression that provides a hard bound for the variance. The bound becomes an equality when the propensities are linear. Furthermore, numerical investigations demonstrate that this is very close to the actual variance also in regimes where the rate of formation of the species is nonlinear.