I don't have a Hudl (instead, a Lenovo Yoga 2) -- but one guess is ... if you are using the Play button on a LibriVox book page, like this one:
Then perhaps it's 'streaming' rather than 'downloading'. The difference is that in streaming, the tablet doesn't save the file, so you can listen immediately, rather than waiting for the whole file to download. This also means there will never
be files to delete -- each one is contained temporarily within the browser, and is tidied away once you close that app. (It's like the YouTube app, or videos you watch on Facebook.
If you really are downloading, that is, are saving the files from our site to play them back later, then I'd recommend using a File Manager (I've used this one for years
.) That will let you look inside folders and delete MP3 files stored. I'd guess they'll be in the Downloads folder, but you can also sort by the folders most recently used, in case it's storing things in your browser folder by default.
Hope this helps, but if not, please do say and we'll try some other things!