What are those cakes called which don't have an icing on them?
In English, all cakes are called just cake, no matter if iced or not. Sponge cake is a name for a cake made from a specific type of batter - it consists of one part fat, one part egg, one part sugar, and one part flour, made by foaming the fat and sugar (with creaming instead of foaming, a batter from the same proportions is called pound cake, at least if you follow the classification established by M. Ruhlmann). You can make other types of cake - angel food cake, chiffon, genoise, etc - and not add icing, they are differentiated by the type of batter only.
In other languages, there is a difference. In German, the ones without icing are called &quot;Kuchen&quot;, and the ones with rich, decorated icing are called &quot;Torte&quot; (and usually seen as a subset of Kuchen&quot;). But in German, a pie is also considered a type of &quot;Kuchen&quot;, so this is more of an umbrella term, even though the standard thing someone pictures upon hearing the word &quot;Kuchen&quot; is some kind of iceless cake, usually on the lines of a marbled Gugglehupf. But in English, there is no special term for a cake without the icing.
In some sources, English speaking authors use a category for the opposite of what you are asking. However, it is not centered on the baking attributes of the cake, but rather on its purpose - I have seen authors create bookchapters called &quot;celebration cakes&quot;, &quot;wedding cakes&quot;, &quot;birthday cakes&quot; etc. It is implicit that they place the richly decorated cakes in these categories, while the plainer ones stay as &quot;everyday cakes&quot;, in UK sources sometimes as &quot;tea cakes&quot; or even get no special name at all. In the end, the same cakes which fall on the &quot;celebration&quot; side in this categorization scheme tend to be the ones that are called &quot;torte&quot; in German.