Preheat the oven to 325 degrees F.
Grease and flour (or add parchment paper to) two 8″ round cake pans and set aside.
In a medium-sized bowl, combine the flour, baking powder, salt and dry instant pudding mix. Whisk well and set aside.
In another bowl, add the coffee creamer, milk, oil and vanilla. Whisk well and set aside.
In a large mixing bowl, add the room temperature butter and mix on medium until smooth. Add in the sugars and mix on medium and then on medium high for several minutes until light and fluffy.
Add in the eggs one at a time and mix on medium for 20 seconds after each egg.
Scrape down the sides of the bowl and mix again on medium speed, just until everything is incorporated.
Alternately add in the flour mixture and the liquid mixture. Starting and ending with the flour mixture. (Add in ⅓ of the flour mixture and mix on medium just until combined. Add in ½ the liquid mixture, mix on medium only until just combined. Add another ⅓ of the flour mixture, mix on medium only until combined. Add in the last of the liquid mixture, mix on medium only until combined, then the last of the flour mixture and mix on medium only until combined.)
Scrape down the sides of the bowl and mix on medium for about 15 seconds. Be very careful not to mix long as that will cause a dense and rubbery cake.
Divide batter into the prepared pans. Batter will be quite thick so just spread it around evenly in the pans.
Bake at 325 degrees F for approximately 50-60 minutes. Ovens vary. Cake layers will bake up flat on top. Make sure not to under bake or the cake will sink in the middle when you pull it out. The cake is done when the sides of the cake pull away from the pan and the top will be a bit firmer and not mushy when lightly touched. (Do not test until very close to the end of the baking time, or this could cause your call to sink.)
Remove the cake layers from the oven and cool, still inside the pans, on a wire rack for about 15 minutes, then turn out onto a rack and cool completely before adding buttercream.