Creating a box and hollowing it is the worst way to skybox a map, purely because it adds extra strain on the engine. Think of it this way: rather than just your map being compiled and rendered, the engine also renders all those gaps under and around your map because it's simply contained in a box.
Think of a skybox as putting a cap, or a roof over your entire map, rather than boxing it. As well as that, did you texture the box with the sky texture?