Wait... it ends in .APE.CUE? That's not a valid file extension, obviously. If you mean you have two kinds of files, one that's .APE and one that's .CUE, that's different. .APE files are an audio format called Monkey's Audio. .CUE files are basically text files that split up a larger audio file into its component parts. So you'll have an .APE album, which is maybe a CD but just in one giant file, then a .CUE file which will attach to that file so that you can skip tracks, etc.
I had a huge thread here about this not long ago. Let me see if I can find it.
...
Bingo.