My computers been randomly shutting down. I've noticed on activity monitor that cached files is almost always at 8GB+, even with no programs running.
Is this a normal value? If not, how do I diagnose what's causing it to run so high?
Yes, that is a completely normal value.
The amount of cached files is not supposed to lower itself when you close running programs. There's no good reason for that to happen. The files will still be cached in RAM ready to be delivered to programs quickly when needed. If they are never needed, they will be purged from RAM eventually.