Butter two 8" cake pans and sprinkle with flour, shaking off excess. Set aside.
In a medium bowl, combine the flour, white and brown sugar, cocoa powder and baking soda. Set aside.
Pour the Dr. Pepper in a small saucepan. Add the chocolate chips and heat over low heat, stirring frequently, until the chocolate is just melted. Remove from heat and set aside.
In a separate large bowl, combine the eggs, buttermilk, oil and vanilla extract. Mix on medium speed until well-combined. Slowly pour in the melted chocolate mixture while constantly mixing at low speed. Add the dry ingredients and mix until well mixed, about a minute or two.
Pour the batter into the prepared cake pans, dividing it equally.
Bake the cakes for 40 - 45 minutes or until the toothpick stuck in the middle comes out clean. Don't overbake. Cool the cakes inside the pans for 10 minutes, then carefully remove from the pans, transfer to a cooling rack and cool completely.
To prepare the frosting, beat the softened butter and the powdered sugar until fluffy. Add the cocoa powder and mix well. Finally, add the Dr. Pepper and the vanilla extract and continue mixing until light and fluffy, about a minute. Set aside.
Once the cakes are cooled down, set the first cake on a serving platter. Evenly spread 1/3 of the frosting on top. Add the second layer and spread another 1/3 of the frosting. Finally, spread the remaining 1/3 of the frosting on the sides of the cake. You may cut and serve immediately.
If using 9-inch cake pans, subtract 10 minutes from the baking time. Similarly, a one inch smaller pan will require additional 10 minutes of baking time.