I found a recipe for a mocha cake that requires the use of espresso powder.  I don’t own any and can’t imagine using it for anything else.  Could I possibly substitute brewed espresso and decrease a liquid (such as the milk or oil)?

Absolutely not. Baking is a precise science, and the liquids you mention aren’t simply liquids. In the case of milk, it has properties such as flavor, fat, lactose (a kind of sugar), and proteins which will affect the outcome of the recipe. Oil in a cake provides lubrication, makes a cake moister and denser, and extends its shelf life. No way can espresso provide any of these qualities in place of milk or oil. Your cake recipe can’t take that kind of alteration and still make a decent cake.

Another reason not to try substituting brewed espresso for espresso powder is flavor. The powder form is much more intense than the brew. No matter how strong you brew a cup of espresso, it will never be as concentrated as the powder.

So bite the bullet and buy espresso powder. It keeps well; and if it does absorb some moisture and solidify, you can break it up and run it through a small coffee grinder (I have an extra I keep on hand for grinding spices, small amounts of bread crumbs, and the like.) If it’s humid where you live, keep it tightly sealed and then put the jar into a Ziploc bag. If you have a vacuum sealer, that would work well, too. Another option would be to purchase packets of food-safe desiccant to put in the jar.

You say you can’t imagine using it for anything else. I can think of quite a few things: in the right quantities, coffee intensifies the flavor of chocolate without adding much of its own, so it’s good in brownies, cookies, cakes,other chocolate desserts. There’s a recipe for espresso biscotti in Wayne Gisslen’s tome Professional Baking (5th edition), and it’s good in tiramisù. It can be used to flavor frostings, buttercreams, puddings, custards, and ice creams. I think it might even be nice used ever so sparingly as a garnish for certain things like vanilla or coffee ice cream. Just don’t use it to make espresso; it’s too concentrated to make a decent beverage. It’s mostly a baker’s secret weapon.