Recursive Bayesian inference has been extensively discussed in recent decades. For Gaussian distributions, the Kalman filter and the Rauch-Tung-Striebel smoother are widely used in fields such as aerospace, robotics, and signal processing. However, for mixture distributions such as Gaussian sums, although prediction and filtering recursions exist, the generic smoothing recursion involves dividing by a density, for which no closed-form solutions are known beyond densities belonging to the exponential family. Instead, many authors decompose smoothing into two filters, one forward and one backward in time. The two-filter approach is not recursive in terms of smoothing marginals, and the backward filter has no moment-form in general. Recently, an analytic solution was proposed for recursively inferring smoothing marginals under mixture distributions. This paper extends that work by providing an explicit closed-form solution for recursive smoothing with Gaussian sums, a problem long considered precarious or even infeasible. Since Gaussian sums can be viewed as universal approximators, the presented approach has substantial applicability, for example in nonlinear and multimodal problems.