I made a yellow cake for my wife's birthday yesterday and it came out fine except that I thought it was a bit tough/dense. Not dry or overcooked. Recipe had four eggs, 3 cups of flour, 1 cup of butter, 2 cups sugar, 1 cup milk and the usual other stuff (salt, baking powder, vanilla).
Might a denser crumb be the nature of this cake/recipe (e.g., nobody expects a light, airy carrot cake)? Or might I have mixed the batter too much/too long with my new Kitchen Aide mixer (a definite possibility)?
You are describing the classic 1, 2, 3, 4 cake that people have been baking for decades. For a lighter cake, you could use cake flour instead of all purpose flour.
You could very well of over mixed as Diane suggests.
I assume you creamed the butter and sugar. If you didn't that would create a heavy cake. The creaming puts some air into the mix and helps the sugar dissolve completely.
There are some other things you can do to lighten a cake but your formula is correct.
When you want to experiment, you could raise the ratio of egg yolk to egg white. Egg white toughen a cake and yolks soften it. An egg is about 2/3 white 1/3 yolk so you could make a 50 50 mix or something like that or 1 less egg white and 1 more egg yolk.
More than likely overmixed. Too much mixing develops gluten, which is fine in bread making, but makes a tough cake. Only fold wet and dry ingredients just barely long enough to combine. In fact, I like to finish combining by hand with spatula.
If you are looking for something to do with leftover cake, you can whip up some pudding and whipped cream, line spring form pan. Layer big chunks of cake, compatible fruit (cherry, blueberies, raspberries, etc), pudding, a little liquor (cognac, brandy, amaretto, etc) and spread some whipped cream on top. Refrigerate overnight and cut in slices. Noone will notice your tough cake.