Unable to move downloaded games on FAT32 External Hard Drive

Hi friends,
That's my problem: When I download games, they get on my local drive C: (NTFS). I would like to move by cut and paste to my external hard drive (FAT32), but will not move because FAT32 does not support more than a certain weight.
I would avoid formatting it because, there is too much paper and I could not put them anywhere.
Do I have to format? If so is that I can format it without losing my files?
Thank you.
