[Rob Milt]"Is it possible two have two completely different hair materials on a single mesh?"
Yes it is. With the desired polygon(s) selected, simply add hair and it will be limited to that selection. A selection tag will be created for the cube, and the "Link" window of the Hair Object will be automatically populated with that selection. The hair that was first added to the cube will appear everywhere else. You can then modify the hair materials individually.