From ehow and also from Gayle’s Step-mother Mary Leighton

Your better option is probably to make it from scratch! Otherwise, this will help.  Adding pudding mix to cake was so popular in the seventies that companies added it at the factory and highlighted “Pudding in the Mix” on the box.
Preheat oven to 350°F and lightly coat the bottom of the cake pan with oil. (You can also use cooking spray or dust the pan with flour.)
ehow version: Combine cake mix and 1 box instant pudding mix in a large bowl. Add ½ cup whole milk (can also use water), ⅓ cup oil, and 4 eggs into mixture.
Mary’s version: uses 1 box instant pudding, ½ cup oil, 1 cup water and 4 eggs. Originally for Duncan Hines Dark Chocolate cake mix (1974).
Most box cake recipes call for ½ or ⅓ cup oil, so the amount of oil is slightly less or around the same. But the amount of water is greatly reduced in this recipe. Most box cake recipes instruct you to use 1 and ¼ cups of water, and this recipe calls only for ½ cup. Whole milk is a recommended substitute for water because it has a thickening effect, but water will still work. The pudding mix and extra egg also produce firmer results.
Blend all ingredients together in the bowl, using either a stirring utensil or a mixer. Blend until the mixture is smooth and has no lumps. It will be thicker than most box cake mixes at this point.