What happens if I use vegetable oil in a cake?
The major difference between butter and oil is that butter is only 80% oil, with the rest being milk solids and water (source).  This means that using oil you will lose some of the water content that your cake should have, possibly resulting in a dryer cake.  On the plus side, cakes made with oil tend to dry out slower than those made with butter.

The other possible different, but one that is unlikely with a mix I'd think, is that it depends on the method of mixing in your fat.  If the butter is to be whipped or creamed while softened this creates a different texture than one you could get with oil or melted butter.  Whipped butter or especially butter creamed with sugar provides a network of air bubbles that act as a raising agent during cooking, and the result is a pound cake like crumb.  If your recipe calls for melted butter, though, this is not a concern - the result is more like a traditional muffin or quick bread crumb.

Finally, a vegetable oil has a fairly neutral taste.  Usually when a vegetable oil is called for, this is desirable.  Butter on the other hand has a more interesting flavor.  Your cake may be a bit bland without it.