Preheat the oven to 180°C (356°F).
Sift coconut flour, regular flour, and baking powder together.
Soften the butter and mix in the sugar.
Add eggs one at a time, mixing well after each addition.
Add the dry ingredients and gradually pour in milk as you mix the batter.
Stir in coconut milk and shredded coconut into the batter.
Pour the batter into the pan and smooth the surface.
Bake in the preheated oven for about 25-30 minutes.
Let cool, then decorate as desired.