Okey dokey, schmokey.
This is a tough one, and I am not going to be able to answer it, but I can give you a little info. If you post your other cake’s recipe, someone might be able to tell you why it was dense-ish. Usually, oil makes for a light, spongy cake (like a cake mix).
Often—usually—a “regular” cake contains some overt fat, like oil or butter. Oil will generally be light and spongy, butter will be a bit more substantial, but neither would be, by definition, dense, unless something else in the recipe caused it to be so.
Eggs can make a super light cake or a dense one, it depends on how they’re handled and mixed, and I don’t know enough about this to explain it.
Also, according to Rose, milk and cocoa powder to not usually go well together in cake—milk brings out the bitterness in cocoa. Usually, in a cake with cocoa powder, cocoa powder is “bloomed” in boiling water, and the water is the cake’s liquid.
Here’s what I would do. I would try this cake: http://www.epicurious.com/recipes/food/views/Maple-Cake-with-Maple-Syrup-Frosting-358216 which is really good. If you want to use cocoa powder—which I wouldn’t, but obviously, everyone’s taste buds are different—instead of using all flour, sub about 1/4 of the flour (maybe a little less) with cocoa powder. Better yet, weight the flour and cocoa powder. The weight the Baked guys (who made this recipe) use for their cakes is somewhere on this site—Flour Girl has it—but I cannot find it. It’s easy to make a cake too dense using volume measurements, beacause it’s easy to use too much flour or flour-like ingredients (like cocoa powder) by accident, as volume measuring is inconsistent.