All occasion cut out cookies

1 package white cake mix
4 sticks butter
2 3/4 cups flour

Gluten free option:
1 package gluten-free yellow  cake mix
3 sticks butter
2 3/4 cups gluten-free flour
1 egg

Icing:
3/4 cup milk
1/2 cup and 1 tablespoon light corn syrup
1 teaspoon vanilla
10 cups powdered sugar
1/2 teaspoon food coloring of choice

Preheat oven to 350 degrees. In small bowl, microwave two sticks of butter for 2 minutes until melted. Slice remaining butter into small pieces, add to melted butter and let stand for 3-5 minutes until softened. In large mixing bowl, whisk cake mix and flour until blended. Whisk butter until very smooth. Pour butter (and egg if using gluten free option) into dry ingredients. Mix to form a smooth dough. Divide dough into three portions. Cover with plastic wrap and refrigerate for 30 minutes. Generously flour a flat surface. Remove one portion of the dough and roll out evenly to 1/8-inch thickness. Cut with desired cookie cutters. Bake 10-12 minutes or until light golden brown. Remove from pan and allow to cool completely. For icing, whisk milk, corn syrup and vanilla in large mixing bowl. Add powdered sugar, whisk until smooth. If icing becomes too thick, add more milk 1 tablespoon at a time. If icing is too thin, add powdered sugar 1 tablespoon at a time. Remove 1/2 cup of icing and place in separate bowl. Add food coloring of choice. Mix well. Decorate as desired. Icing will set in 3-4 hours.