Not easily.
You can swipe on individual books in the book list and select "Share books or annotations", then "send to". You can then save it to drop box or something similar.
It was intentionally limited to single books to prevent easy pirating - among other reasons.
Best bet is to keep
multiple back-ups. Also, your calibre library might not be a total loss. I'm sure there are possible recovery options. Ask in the Calibre forum and they might be able to help.
Cheers,