Preheat oven to 350 degrees F. Coat the insides of five 8-inch by 2-inch round cake pans with nonstick spray, line bottoms with parchment rounds, then spray parchment.

Whisk together flour, baking powder and salt in a medium bowl to combine and aerate; set aside. Whisk together the egg whites and milk in a small bowl until thoroughly combined; set aside.

In a large bowl with an electric mixer on medium-high speed, beat butter until creamy, about 2 minutes. Add the sugar gradually and beat until very light and fluffy, about 3 minutes, scraping down the bowl once or twice. Beat in vanilla.

Add the flour mixture in four additions, alternately with the egg white/milk mixture. Begin and end with the flour mixture and beat briefly until smooth. Scrape a generous 2 ¼ cups of batter into one of the prepared pans and level the top with a small offset spatula; this will be your lightest colored layer. Add a tiny bit of food coloring to the remaining batter, blending well until the color is the same throughout. Scrape another generous 2 ¼ cups batter into another pan, leveling that batter as well. Keep adding tiny amounts of coloring to the batter (use photo as inspiration) with each subsequent layer until you have used up all the batter and you have 5 distinctly colored layers.

Bake for about 30 minutes or until a toothpick shows a few moist crumbs. The edges will have just begun to come away from the sides of the pan. Cool pans on racks for 8 minutes. Unmold, peel off parchment, and place directly on racks to cool completely. Layers are ready to fill and frost. Alternatively, double wrap in plastic wrap; store at room temperature if assembling within 24 hours. Layers may be frozen for up to 1 month. Defrost in refrigerator overnight before proceeding.

NOTE: You will be making 2 batches to have enough buttercream for icing the cake. The ingredient list has the amount for both batches of buttercream in total. Once you have completed 1 batch, repeat with remaining ingredients.

Puree 2 of the raspberry packages (6 ounces) in food processor fitted with metal blade. Press through a fine meshed strainer; you should have about 1 cups seedless puree. Set aside.

Place 1 1/4 cups of sugar and water in a small pot. Stir to wet sugar. Bring to a boil over medium-high heat, swirling pan occasionally. Dip pastry brush in cold water and wash down sugar crystals from the sides of the pot once or twice. Allow sugar mixture to boil rapidly as you proceed with egg whites. Bring the sugar/water mixture to a rapid boil and cook until it reaches 248 to 250° F.

Meanwhile, place egg whites in clean, grease-free mixing bowl and whip until frothy on low speed using balloon whip attachment of standing mixer. Add cream of tartar and turn speed up to medium-high. When soft peaks form, add 1/3 cup sugar gradually. Continue whipping until stiff, glossy peaks form.

When syrup is 248 to 250 degrees F pour a thin, steady stream directly over egg white meringue. Do not pour any onto the whip attachment or the sides of the bowl. Whip the egg white meringue until cool to the touch; this step is very important and may take several minutes. With machine running, add butter a couple tablespoons at a time. Keep beating until the buttercream is completely thick, spreadable and smooth. Remove 2 1/2 cups of buttercream and set aside for your lightest buttercream.

Repeat steps and make second batch. Combine both batches together (they will now fit in the 5-quart stand-mixer bowl), turn machine to low speed and add ½ cup raspberry puree. Gradually increase speed and whip until raspberry puree is incorporated and buttercream is smooth and pale pink. Remove 5 cups of buttercream and set aside; this will be for lightest pink filling and crumb coat. Add an additional ¼ cup raspberry puree to the buttercream and beat until smooth then also add more puree if necessary to make it slightly darker than the last batch. Beat until smooth; remove 2 ½ cups and set aside. Add more raspberry puree and a little food coloring (start with 1/16th teaspoon), beat until smooth, remove 2 ½ cups and set aside. Tint remaining buttercream in mixer a little darker. Your amount of raspberry puree and food coloring might vary; just make 5 distinct batches.

Have cake layers and buttercream ready to use. Level any of the cake layers if necessary with a large serrated knife. Place darkest layer on cardboard round. Spread a thin even layer of darkest pink buttercream on top of cake layer all the way to the edges. Place second darkest pink cake layer on top, repeat with second darkest pink buttercream, then continue to build cake with each subsequently lighter pink cake layer. When the last layer is in place, apply a thin coat of the palest pink buttercream all over the top and sides of cake. Chill cake briefly at this point to firm first coat of buttercream.

To finish icing, remove cake from refrigerator and starting at the bottom, ice cake with darkest buttercream, matching shade of icing to shade of cake layer moving up to lightest layer of buttercream on top. Finish icing top of cake with lightest buttercream Refrigerate cake at least 2 hours to firm up buttercream, or up to 2 days under a large cake dome. Bring to room temperature before serving. Place mound of fresh berries on center top of cake right before serving. Serve each slice with remaining raspberries.