Follow the steps provided in this support guide:
If you still can't backup your iP6+ using iCloud, connect your device to a computer running iTunes latest version, and perform the backup : How to back up your iPhone, iPad, and iPod touch - Apple Support
If you don't have a computer, borrow one from your friends, or go to the nearest Apple Store or Authorized Service Provider: Apple - Find Locations - Location Selector
Your data are important, so find a way to have them in a safe place.
Regards and best of luck.