Chocolate-bar games are variants of the Chomp game. Let Z≥0 be a set of nonnegative numbers, and let x, y, z ∈ Z≥0. A three-dimensional chocolate bar is comprised of a set of 1 × 1 × 1 cubes with a “bitter” or “poison” cube at the bottom of the column at position (0, 0). For u, w ∈ Z≥0 such that u ≤ x and w ≤ z, the height of the column at position (u, w) is min(F(u, w), y) + 1, where F is an 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 the function f for a two-dimensional chocolatebar game such that the Sprague-Grundy value of CB(f , y, z) is y ⊕ z. In this study, we characterize the function F such that the Sprague-Grundy value of CB(F, x, y, z) is x ⊕ y ⊕ z.