The name coffee cake can mean a cake flavored with coffee, or a cake intended to accompany a cup. That difference helps explain the variety of recipes gathered under the term. The source contrasts coffee-flavored sponge styles with crumb-topped cakes, then presents a variation incorporating coffee and Baileys.
For a coffee-flavored cake, dissolve or prepare the coffee as the complete recipe specifies so it distributes through the batter. Mix and bake according to that formula rather than adding an arbitrary splash to another cake. The source's loaf example uses an oven setting of 350 degrees Fahrenheit and approximately forty minutes, followed by cooling; those figures belong to that recipe and pan, not every cake in the category.
A crumb topping, an icing and a liqueur addition each change the overall balance. If the cake will be served with coffee, consider whether the pairing becomes overwhelmingly sweet or whether the drink provides a useful contrast. Check the full ingredient list and serving requirements before adapting it for dietary needs. Clear naming makes the recipe easier to choose and gives guests a more accurate expectation.

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