There are several different types of champagne cake, and not all actually contain the sparkling wine. In some recipes, it's a white cake with champagne added to give the cake an extra spark or bubble. Many people are familiar with the pink champagne cake, which is a white layer cake filled with either Bavarian cream or rum custard, and frosted with pink butter cream icing.
It is hard to trace the origins of this cake, but it is typically associated with retail bakeries, and probably derives from other cakes that would have used a Bavarian cream or custard filling. Occasionally, people will find one filled with whipped cream as opposed to the more common fillings, but this largely depends on the bakery preparing the cake.
Most variants of champagne cake, whether pink or white, begin with a white layer cake. In bakeries, of course, a customer can order sheet cakes for large numbers of people hungry for the dessert, but the typical presentation is a round cake of two or three layers.
Typically, the cake body should be light and frothy, although it is hard to duplicate effervescence in cake form. This may be why some bakers turned to rum flavored custard, to give the cake a somewhat alcoholic taste. People who like the taste of rum, but not the alcoholic content, should know that most commercial custards are made with rum flavoring. Like vanilla extract, the rum flavoring has a small amount of alcohol, but it is relatively small as compared to adding real rum.
For the purist, the rum custard typically used in this cake should contain real rum. In addition, the cake may receive a small coating of rum prior to adding the custard in a way that is similar to the many Italian cakes that are soaked or at least sprinkled with rum. As an alternative to custard, rum flavored whipping cream, or Bavarian cream — custard with whipped cream folded in — can produce a very fluffy filling.
Typically, the cake is topped with curled shavings of white chocolate, or in the case of pink champagne cake, white chocolate that has been dyed pink. This is added after the cake is completely frosted with butter cream icing.
It's also possible to make a chocolate champagne cake, which typically has the same filling options, but is made with a light chocolate cake instead of a white base. The cake body tends to be heavy on egg whites so it is both fluffy and moist. It's often topped with regular chocolate shavings.
Champagne cake appears to be making something of a comeback in recent years. It has become quite popular as a wedding cake and adapts well for this purpose. The cake often matches well with a traditional dry champagne.