Summary: Chocolate-bar games are variants of the Chomp game. Let \(Z_{\geq 0}\) be a set of nonnegative numbers and \(x, y, z \in Z_{\geq 0}\). A three-dimensional chocolate bar is comprised of a set of \(1 \times 1 \times 1\) cubes, with a “bitter” or “poison” cube at the bottom of the column at position (0, 0). For \(u, w \in Z_{\geq 0}\) such that \(u \leq x\) and \(w \leq z\), and the height of the column at position \((u, w)\) is \(\min(F (u, w), y) + 1\), where \(F\) is a monotonically increasing function. We denote such a chocolate bar as \(CB(F, x, y, z)\). Two players take turns to cut the bar along a plane horizontally or vertically along the grooves, and eat the broken pieces. The player who manages to leave the opponent with a single bitter cube is the winner. In a prior work, we characterized function \(f\) for a two-dimensional chocolate-bar game such that the Sprague-Grundy value of \(CB(f, y, z)\) is \(y \oplus z\). In this study, we characterize function \(F\) such that the Sprague-Grundy value of \(CB(F, x, y, z)\) is \(x \oplus y \oplus z\).