Preheat oven to 350 degrees and line a muffin pan with white cupcake liners. In a large bowl, using a hand blender, mix together the eggs, butter, yogurt and milk. Add the dry cake mix and blend until the mixture becomes a smooth batter.
Divide batter evenly into three small bowls. Squeeze one drop of natural blue dye into one bowl, three drops into another bowl and six drops into the third bowl of batter. Place one teaspoon of each color of batter into the cupcake liners, beginning with the lightest color and ending with the darkest batter color on top. Use the back of a spoon to smooth out each layer evenly to the edges of the cupcake liner.
Bake 15 minutes, until the cupcakes are firm to the touch and a toothpick inserted into the center comes out clean. Cool completely on a wire rack.
To make the frosting, blend together the butter and yogurt in a small bowl until creamy. Slowly add the dry frosting mix and whisk until smooth. Divide frosting evenly into three bowls. Add 2 drops of red dye to one bowl, 2 drops of yellow into the next bowl and 2 drops of pink into the third bowl. Blend each bowl of frosting to evenly distribute the color.
Place a disposable piping bag with a star tip into a drinking glass and fold the edges of the bag over the lip of the glass. Using a spatula, place spoonfuls of each color of frosting into the piping bag side by side. Squeeze frosting down to the tip of the piping bag and twist the top closed then frost each cupcake.