1. Preheat the oven to 350°F (175°C). Grease and flour three 8-inch round cake pans.
2. Mix dry ingredients: In a large bowl, combine the cake flour, sugar, baking powder, salt, and dry pudding mix.
3. Add wet ingredients: Add the softened butter and mix with a hand mixer or stand mixer until the mixture resembles coarse crumbs.
4. Add coconut milk and buttermilk: Mix in the coconut milk and buttermilk until smooth.
5. Whisk egg whites and egg: In a separate bowl, whisk the egg whites and egg until frothy. Add to the batter and mix until combined.
6. Add coconut extract: Stir in coconut extract for added flavor.
7. Pour batter into the prepared pans, dividing evenly.
8. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
9. Cool the cakes in the pans for 10 minutes before transferring them to a wire rack to cool completely.

For the Frosting:

1. Beat together the softened butter and cream cheese until light and fluffy.
2. Gradually add the powdered sugar and beat until smooth.
3. Add the milk and coconut extract, and mix until fully incorporated.

For the Simple Syrup:

1. In a small saucepan, combine the water and sugar. Bring to a simmer and stir until the sugar dissolves completely. Remove from heat and let cool.

Assembling the Cake:

1. Once the cakes are cooled, brush each layer with simple syrup to keep the cake moist.
2. Frost each layer with the cream cheese frosting, and stack the layers.
3. Cover the top and sides of the cake with frosting.
4. Garnish the cake with sweetened or flaked coconut on top and around the sides.