Prepare cake mix according to directions on package and set batter aside.
In a large, separate bowl, combine dry ingredients and mix together. Cut in softened butter or margarine until blended well.
In a small bowl, beat egg and milk together and add to dry ingredients. Stir just until blended. Add cake batter to cornmeal mixture and blend thoroughly.
For cornbread squares: Add batter to 13x9 inch baking pan that has been sprayed with nonstick cooking spray and floured. Fill pan 2/3 to 3/4 full. (There will be a little extra batter left for muffins.)
Bake at 350 F. for 30 - 35 minutes.
For cornbread muffins: Add batter to muffin tins sprayed with nonstick cooking spray and floured or add batter to paper muffin cups. Bake at 350 F. for 18 to 23 minutes.