Can a third party cloud backup app backup all user accounts on my Mac? I use an app called LiveDrive to backup my Mac running OS X 10.9.5. It provides incremental Cloud backup. 

My user account is an administrator and it is under this account that the LiveDrive backup software runs.  I have found that only files in my user account (Desktop, Documents etc) are backed up by this software. There are 3 other user accounts for other family members which I would also like backed up.  I have added folders e.g. /Users/Child1/Documents, /Users/Wife/Documents to the backup software's list of backup locations, but files in these locations never get uploaded to the Cloud. I assume because the backup software (like my user account) does not have permission to view other users' files.

So is there a way to get the backup software to backup all users' files?

Note: I am trying to avoid purchasing 3 more licenses for LiveDrive. I could use Time Machine but I don't have an external HD to set that up and would prefer backups to be stored remotely.
I have the same requirement !  This FAQ seems to indicate Backblaze backsup other user accounts. I have yet to verify it though ..

https://help.backblaze.com/entries/26264869-Does-Backblaze-back-up-my-other-user-accounts-on-my-computer-