Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla.
In a separate bowl, whisk together the flour and baking powder. Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry ingredients. Beat until just combined.
Stir in the blue food coloring until the batter is evenly colored.
Pour the batter into the prepared pan and bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes before inverting it onto a wire rack to cool completely.
For the frosting, cream together the butter and powdered sugar until light and fluffy. Gradually add the milk and vanilla extract, beating until smooth.