Well it could be the phone has no space for the download. It could be a bad download. Bad location you are downloading from, etc.
Have you tried restarting (turning off and back on) the phone to see if perhaps they did download and just didn't show until the restart? Happens a lot. Also, these files would not download to whatever music folder you have, unless you set the app you are downloading them through to download to that folder. So they may be somewhere you aren't looking for them.
To check you can either use the file manager app on the device (if it has one) or connect the phone to a computer via USB cord and try searching for any of the files.
Also, please note, if the files are not a type that the phone can play, then you may not see them through any app that is meant for playing say music, etc. So make sure they are file types your phone can play and be careful where you download from.