We consider a linear Volterra integral equation of the second kind with a sum kernel Kpt 1 , tq " ř i K i pt 1 , tq and give the solution of the equation in terms of solutions of the separate equations with kernels K i , provided these exist. As a corollary, we obtain a novel series representation for the solution with improved convergence properties. We illustrate our results with examples, including the first known Volterra equation solved by Heun's confluent functions. This solves a long-standing problem pertaining to the representation of such functions. The approach presented here has widespread applicability in physics via Volterra equations with degenerate kernels.