<p>In this paper, we extend the classical functional equations (such as the square, rectangle, and cube equations) to the hyperrectangle functional equation in the more general setting of groups. Using mathematical induction, we determine the explicit forms of the central solutions to this equation. The hyperrectangle functional equation naturally unifies and generalizes the Jensen-type and rectangle-type functional equations to functions of several variables. In particular, our results provide a unified characterization of the solutions for an arbitrary number <i>n</i> of variables.</p>