Most probably, when you mount the drive, it gets mounted as root so your normal user privileges are insufficient. If you have added an fstab entry for your drive, you can set an option "umask=022" to give all users permission to access the drive (write there).
But what is the error you encounter? Do you get some kind of error message? If you haven't added an fstab entry yet, I suggest you do so: become root and edit your /etc/fstab file, and add the following line there (or edit the existing one):
/dev/sda1 /mnt/usbdrive vfat users,rw,umask=022 0 0
Then save and try
after which try to copy mp3's onto the drive. Once done,
then wait a bit so the data is written on the drive and you should be fine. But if it's not about permissions, please post here the error message you get when trying to copy mp3 files on the drive, so we can give more help