Heat oven to 350 degrees F. Coat 3 large cookie sheets with nonstick cooking spray.
In large bowl, combine cake mix, eggs, oil, 3 tablespoons water and baking powder. Beat on low speed for 30 seconds, then on medium for 2 minutes; batter will be thick. Drop by heaping tablespoonfuls onto prepared sheets, spacing about 2 inches apart, for a total of 36 mounds.
Bake at 350 degrees F. for 12 minutes, rotating sheets halfway through. Let cookies stand on sheets for 2 minutes, then use a thin metal spatula to quickly transfer cakes to wire racks to cool. Repeat with remaining batter.
While cakes are cooling, prepare filling. In a medium-size bowl, beat butter until smooth. Add confectioners' sugar, vanilla and 1 1/2 tablespoons water. Beat on low speed until blended, then increase speed to medium-high and beat until smooth. Spread a heaping tablespoon filling onto a cake. Sandwich with a second cake. Repeat.