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Preheat oven to 350°F. Prepare 1 of the white cake mixes as directed on package, adding lemon extract. Divide cake batter evenly among 5 bowls (about 3/4 cup batter per bowl). Stir 1/2 teaspoon food color into each bowl as follows: add neon pink to one bowl, orange to the next (1/4 teaspoon yellow, 1/4 teaspoon red), yellow to the next, green to the next, and blue to the last bowl.
Place medium resealable plastic bag in tall drinking glass with top of bag draping around outside edge of glass. Pour pink batter into bag. Remove bag from glass. Twist bag, then secure with twist-tie or rubber band. Set aside. Repeat with remaining 4 colors.
Line baking sheet with parchment paper. Cut off 1/4-inch piece from tip of 1 of the corners of pink bag. Pipe 1/4-inch thick line of batter lengthwise on parchment paper. Repeat with all the colors until parchment paper is completely covered in lines of batter. Lines of batter should be touching each other. (Place bags of batter in separate glasses to keep them upright while piping out each color.) Use a second baking sheet if necessary so that all of the batter is used.
Bake 8 to 10 minutes or until edges of cake start to brown. Cool completely on wire rack.
Using an egg-shaped cookie cutter (about 2 1/2 inches across and 3 inches high), cut out egg shapes from the striped cake.
Prepare remaining white cake mix as directed on package. Pour about 1 cup of batter into 9x5-inch loaf pan sprayed with no stick cooking spray. Place striped cake eggs standing up along center of loaf pan so that the entire center of pan is filled with a line of cake eggs. (Cake eggs should be touching. Do not leave any spaces between them or the white batter will seep in between.) Carefully pour remaining white batter into pan, filling in sides first then pouring over top of cake eggs.
Bake 40 to 45 minutes or until toothpick inserted into white cake comes out clean. Cool in pan 10 minutes. Remove from pan; cool completely on wire rack.
For the Buttercream, beat butter and vanilla in large bowl until light and fluffy. Gradually add confectioners' sugar, beating well after each addition and scraping sides and bottom of bowl frequently. Add milk; beat until light and fluffy. Stir in red food color until desired shade is reached. Frost top and sides of cake with Buttercream.