The nonlinearities in a dynamic system and its measurement equations are assumed to be cubic and small, i.e., all proportional to a single scalar small parameter \(\epsilon\). The optimal digital nonlinear feedback control law is carried through the first power of \(\epsilon\), taking into account the non-Gaussian character of the state conditional distribution. The optimal law involves cubic and linear terms in the state estimate, as well as higher moments of the state conditional distribution.