Prepare and bake cake mix according to package directions for one 9x13 inch cake. Remove cake from oven. Poke holes at once down through cake to pan with the round handle of a wooden spoon. Holes should be at 1 inch intervals.
Combine the pudding mix with the confectioners' sugar and gradually stir in the milk. Beat with an electric mixer at low speed for not more than 1 minute. Do not over beat. Quickly, before pudding thickens, pour about 1/2 of the thin pudding evenly over the warm cake and into the holes. (This will make the stripes in the cake.) Allow the remaining pudding to thicken slightly then spoon over the top, and spread to frost the top of the cake. Chill for at least 1 hour before serving. Store leftovers in the refrigerator.