Sift together cake and pudding mix. Whisk in remaining ingredients until smooth. Mixture will be somewhat thick.
Line a cupcake pan with liners. Fill liners 2/3 full of cupcake mixture.
Bake for 20-25 minutes or until toothpick inserted in the middle of cupcakes comes out clean. Cool completely.
To make the frosting, beat the butter with a hand held mixer. Continue beating as you gradually add in the powdered sugar. Add in the milk and coffee until frosting is stiff but spreadable