Preheat the oven to 180 ºC (356 ºF)
Add and combine the white rice flour, tapioca flour, corn starch, brown rice flour, xanthan gum, baking powder, baking soda and salt. Set the dry ingredients aside.
Using a standalone mixer, with the paddle attachment fitted or handheld mixer, beat the butter, cream cheese, sugar at medium-high speed until creamy (1-2 minutes). Then add the eggs one at a time, mixing until incorporated with each addition. Then, add the vanilla extract and mix until combined.
Add ⅓ of dry ingredients followed by ⅓ of the buttermilk and mix until combined. Repeat two more times until the vanilla cake batter is formed (1-2 minutes). Do not overmix the batter. The cake batter will be thick.
Scoop ½ cup of vanilla cake batter and add the cocoa powder and milk to it. Whisk until just combined.
Grease a standard-size bundt pan with butter. Pour ⅓ of the vanilla cake batter into the bundt pan. Then drizzle some of the chocolate cake batter on top. Repeat two more times.
Bake, the gluten free marble cake for 35-40 minutes or until a toothpick inserted at the center comes out clean.
Let the cake cool down in the bundt pan for 10-15 minutes before inverting it. Then, flip the cake onto a cooling rack and let it cool down to room temperature before storing.