APE (also called Monkey's Audio) is a lossless audio format like FLAC. Foobar2000 does not ship with support to playback APE files.
To play APE files with Foobar2000, download and install the Monkey's Audio Decoder component. This component ships as a DLL file named
foo_input_monkey.dll (For instructions on installing Foobar2000 components, see here.)
Tried with: Monkey's Audio Decoder 2.1.5 and Foobar2000 1.1.1