Concept:For a cube of side n painted on all faces and cut into 1×1 unit cubes, cubes with only one colored side come from the center of each face, excluding edges.Explanation:Number of such cubes per face = (n−2)2.There are 6 faces, so total = 6(n−2)2.Check options: 6(n−2)2=216 gives (n−2)2=36, so n−2=6, n=8.Other options do not yield integer n (e.g., 125 gives n−2=125/6​ not integer).Answer:216