If the power goes off unexpectedly, the server would have to power to write that into a log.
I think the best you can probably do is check when the last entries in the "/var/log" files were made. That would give you approximate time of shutdown. And, might give you a clue as to what was running when it died. If you are wondering about it being a hardware failure, knowing when it died and what was running might help you track down the problem.
If it was a simple power failure, then without a battery backup which can communicate with the server itself, there's no way I know of to know when exactly the system shut down.