How to put a backup on the cloud

I have all filled up hard drives and need to move files to the cloud. Can I do the same with my ITunes Library and not loss the massive content I have nearly 30GB. If I have to load it to my dropbox, it may take the 10+ days and tie up my PC and internet for way too long. What's the safest and reasonably timely way to do this?

Thanks,

Rose