I've found two methods to make my homemade cake taste "just like store-bought" -- so, being me, I usually avoid these techniques unless the birthday person prefers bakery cake or cake mix.
First, for the base cake, use lots of cheap, artificial vanilla. I prefer real vanilla, but the kind that doesn't even taste much like true vanilla extract manages to impart a taste of not-made-at-home. [By lots, consider doubling the amount in your recipe.] I use this simple white cake or Hershey's Deep Dark Chocolate Cake.
Second, for the icing, use a stand mixer. Extra beating time means extra fluffiness, more like store-bought icing. (The chocolate cake link includes a recipe for icing; replace the cocoa with extra powdered sugar for white icing.) I do like fluffy icing, so I actually make icing this way.