A recipe for a simple gluten-free mayonnaise cake is AllRecipe.com's Gluten Free Chocolate Cake using gluten-free flour. If an egg allergy is also an issue, substitute egg-free mayonnaise for regular mayonnaise.
To make AllRecipe.com's Gluten Free Chocolate Cake, start by mixing together 3 cups gluten-free flour, 2 cups sugar and 1/3 cup cocoa powder with 2 1/4 teaspoons baking powder and 1 1/2 teaspoons baking soda and 1 1/2 teaspoons xanthan gum. Add in 1 1/2 cups mayonnaise, then gradually pour in 1 1/2 cups hot water. Stir in 1 1/2 teaspoons vanilla extract until smooth. Pour batter into two 9-inch greased cake pans, and bake for 30 minutes at 350 degrees Fahrenheit. Cool in the pans for 10 minutes, then cool completely on a wire rack before topping with desired frosting.
For a yellow gluten-free mayonnaise cake, combine 1 1/2 cups rice flour, 3/4 cup tapioca flour, 1 teaspoon salt and 1 teaspoon baking soda, 3 teaspoons baking powder, and 1 teaspoon xanthan gum. Mix together four eggs, 1 1/4 cups sugar and 2/3 cup mayonnaise. Add the dry ingredients, 1 cup milk and 2 teaspoons vanilla to the egg mixture. Pour the batter into greased 9-inch round cake pans, and bake for 25 minutes at 350 degrees Fahrenheit. Cool completely before frosting.