Will iPod Classic play .aiff files?

I have a bunch of .aiff files I bought and downloaded from the Bandcamp website to my desktop mac. Some are 16 bit/44.1 Khz. and others are 24 bit/96 Khz.

The 16/44 files synced/transferred to my ipod Classic 160 Gb., but when I try to play them, the ipod simply goes directly to the next song on the playlist.

The 24/96 files didn't even sync/transfer to the iPod, and there was no dialogue box saying there was a problem.

No problem playing these files on my iphone and with bluetooth from iphone to earbuds.

Is there a problem with my iPod? Or is it the file format?

I had some problems with my iPod, and I had to reformat it, a process that required many redos, but I thought everything was working ok.

Thanks!