Can I attach both an 4 AWG and an 8 AWG Power cable to the same terminal lug?

I wouldn't do it....because you'll spend more time fighting it rather than buy some new 1/0 power wire and keeping it simple for yourself.

Like Boomin said, you may have issues getting both to fit inside the lug and you will end up with a half-ass crimp.  But if both wires slide all the way in without fighting and/or having to remove strands and you can get a good solid crimp then I don't see any reason why you can't.  I'm sure you have seen some pretty cheezy connections people have done when wires don't fit properly.......you just don't want one of those.

No don't do it that is what distribution blocks are made for and they come with their own fuses as well. You can buy those with 2 100 amp fuses for around 10-15 bucks on amazon or eBay. Doing 2 wires is one of the worst redneck things you can do. Do it right the 1st time with the right equipment instead of doing things half-assed.

Mate, you can go ahead but you are setting yourself and your car at risk including the passengers.  Use correct gauge wires and distribution blocks , none of that backyard butcher jobs :crying:  that is done when they don't have access to correct gear.    Don't do it mate!!!

Better running a small amp with your current power wire kit then installing a huge amp with small power as it will draw more current and could melt the wires not to mention, could cause fire to your vehicle.  If you don't have to dough, then save up but do it correctly as mistakes like this will not be covered by our car insurance agency as well :uhoh:

Insurance companies are always looking at this possible causes so they can reject your claim in an event of an accident.  :furious:

If you are not sure, then ask your car audio shops to provide guidance to do it, or if you are not competent then ask them to do it for you as their work is guaranteed under the industry legislation.