For the cake: Preheat the oven to 350 degrees F. Grease two 9-inch round cake pans with butter and line the bottom of each with parchment.
Whisk together the flour, baking powder and salt in a medium bowl. Whisk the milk, vanilla, eggs and egg yolk together in another medium bowl. Beat the butter and sugar in a large bowl with an electric mixer on medium high until light and fluffy. Add about a third of the flour mixture and beat on medium low until incorporated. Now add a third of the egg-milk mixture and continue to beat on medium low until incorporated, scraping down the sides of the bowl as needed. Repeat with the remaining flour and egg-milk mixtures, finishing with the flour.
Divide the cake batter evenly between the prepared cake pans and bake until the cake bounces back when pressed and a toothpick inserted in the center comes out clean, 35 to 40 minutes. Let cool completely in the cake pans on a rack.
For the frosting: Bring a few inches of water to a boil in a saucepan that can hold a heatproof stand mixer's bowl above the water.
Add the sugar, lemon juice, salt and egg whites to the mixer bowl and whisk together by hand. Set the bowl above the boiling water and whisk until the mixture is warm to the touch and the sugar completely dissolves. Transfer to the stand mixer fitted with the whisk attachment and beat at medium-high speed until cool and the whites hold stiff peaks, 10 to 15 minutes.
Toss in a couple of chunks of butter at a time, making sure the pieces are incorporated before adding more. After all the butter is added, continue beating on medium-high speed. The mixture will deflate and appear curdled. Continue beating until the frosting comes back together to a smooth and spreadable consistency. (If the frosting is very soft or begins to break, refrigerate until set but still spreadable, then beat until light before using.)
For the filling and decoration: Dye the coconut: Have ready 5 resealable plastic bags or plastic containers. Put 1 1/2 cups of the coconut in one container with 6 to 8 drops of blue food coloring. Put 1 cup of coconut in the second container with 5 to 6 drops of orange food coloring, 1 cup of coconut in the third with 5 to 6 drops yellow food coloring and 1 cup of coconut in the fourth with 6 to 8 drops purple food coloring. Put the remaining 1/2 cup coconut in the fifth container with 4 to 5 drops pink food coloring. Seal each container and shake vigorously until the coconut is evenly dyed. Add more food coloring 1 drop at a time as needed to get bright, vibrant colors.
Assemble the cake: Cut a 4-inch circle out of the center of each cake (reserve the small cut-out cake rounds). Put one of the cake rings on a cake stand or serving platter and frost with about 1 cup of frosting. Put the other cake ring on top and push down slightly. Fill the hole with candy. Cut one of the reserved cake rounds in half horizontally to make 2 thinner rounds. Use one to fill the hole on top of the cake. Frost the top and sides of the cake with the remaining frosting.
Cut a strip of parchment about 30 inches long and 3 inches wide. Wrap this parchment around the cake like a collar, leaving 1 inch of frosting exposed around the bottom perimeter of the cake. Pack some of the blue coconut onto the exposed frosting to make your first strip of color. Lift the collar up another 1 inch and do the same with the orange coconut. Remove the collar and fill the remaining inch of frosting with the yellow coconut. For the top, make 1-inch-wide rings, starting on the outside and working your way in, with the purple, pink, blue and orange coconut until the top is completely covered. Let sit at room temperature for at least 1 hour before serving.
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