To make the cake, preheat the oven to 375°F (190°C). Line 17x11in (43x28cm) deep baking sheet with a parchment paper and spray cooking spray all over the parchment paper and on the sides. Alternatively, you can use silicone mat in place of parchment paper.
In a mixing bowl with a paddle attachment, mix together eggs, milk and melted butter until well combined. Add cake mix and mix just until combined.
Pour the batter into the prepared baking sheet and tap a few times to get rid of bubbles. Bake for 15-18 minutes, or until the inserted toothpick comes out clean.
While the cake is cooling, make the frosting. Beat butter and cream cheese on medium high speed until fluffy for 1 minute. Add powdered sugar, heavy cream and vanilla extract. Beat on low speed for a minute. Then increase the speed to medium high and continue to beat until smooth and fluffy, about 3 minutes. Transfer into a piping bag.
For decoration, sort the M&Ms by color (you’ll need about 2 tablespoons of each color) and crush them with a rolling pin until desired fineness. Set aside.
To assemble, once the cake is cooled completely, cut out 2-inch circles using a round cookie, or biscuit cutter. You should get 40 circles. Place the cut out cake circles on wire rack. Pipe about heaping tablespoon of frosting on half of the cake circles. Using an offset spatula lightly spread the frosting. Then top with remaining plain cake circles. Frost the second layer the same way and finish with crushed M&Ms. To arrange the cakes in flag pattern, you’ll need 4 blues, 8 reds and 8 whites.
Mix the leftover cake scrapes and buttercream frosting in the mixing bowl with paddle attachment, or using a handheld electric mixer, and make some cake pops.
Store the cake in a fridge, covered, for up to 3 days.