how do you open .ape and .cue files?

A CUE file must be accompanied by a BIN file. The CUE file states the contents of the BIN file. The BIN file is the CD/DVD image in binary data. These files can be opened by burning software such as Nero, Roxio, imgburn, ISObuster, etc.
Download the free version of ISOBUSTER
http://www.smart-projects.net/license-models.php
How to open a CUE File, check http://www.ehow.com/how_4442813_open-cue-files.html
How do I Open or Mount a Bin File Without a Cue File? http://www.tech-recipes.com/rx/881/how-do-i-open-or-mount-a-bin-file-without-a-cue-file/

APE file is associated with sound or music files compressed with Monkey's Audio or it can be a plugin for Winamp.
In case it's a music file, then you need Monkey's Audio or with the appropriate codec other media players can open the APE files, like Winamp, JMAC, Media Monkey and Windows Media Player . The codec pack need to open a APE file is K-lite, get it at http://www.codecguide.com/about_kl.htm

APE is a lossless audio format. Unfortunately, it has very limited software support.

I use foobar2000 on Windows to play APE directly, but many people just prefer to transcode it to FLAC or even MP3 so they can use some other program.

You can get foobar2000 for free though here: http://www.foobar2000.org/?page=Download

To play APE in foobar2000, you need to install the Monkey's Audio decoding support plugin at the top of the list of optional components.

What Is An Ape File

I was wondering the same thing myself today

Hi there,
I use Isobuster and it works fine. I got it here http://bitly.com/1k4nMIw
It's a useful program
Have a nice day