iOS Software Update over cellular data

How can I software update over cellular data? I've got enough data on my SIM but when go to update my iPad to iOS 8, it requires Wi-Fi. I do not have a router.

Apple doesn't allow major iOS updates over cellular. You can update from 10.3.1 to 10.3.2 over LTE, but not from 10.2 to 10.3.

This is not a technical limitation of cell data or wifi, per se, but rather a policy limitation (though some carriers have limits of how big individual files transmitted over their networks can be). Major OS updates can run into the gigabyte range, and while many users have multi-gig or unlimited data plans, not all users do - so updates above a given size are disallowed, per manufacturer policy, from downloading over cellular.

If you hotspot your phone and download the update to your laptop, then run the install via iTunes, you can get around it. Or if you find a wifi connection elsewhere (that won't cut you off for excessive data use (as some free/public ones can/will)).

Side note:

It's - generally - fastest to do OS updates via iTunes from your computer, because the update does not have to download to your phone, then extract, then install, then clean up after itself (especially important to consider if you only have 3G free on your device, but the update download size is 4GB: the update will likely still install if you do it via iTunes, because it will be overwriting existing files (along with removing some and adding some) on the phone, using your laptop/desktop as its workspace for extracting the update archive).

All the above will not work. What you will need for this are two things: your iPhone, and a Mac or windows PC, with iTunes installed. After that, tether data from your iPhone to your Mac. Your Mac will believe it is a wireless connection. Then, launch the iTunes app from your laptop, and download and update your phone. Make sure, obviously, that your phone is connected via USB.