Is it possible? I've tried about 5 games now on King... large map... I get hopelessly behind. I've won King with every other leader... but man... he just sucks.
Kamehameha sucks when he's controlled by the AI, but when you control him, and have the right map (i dont think pangea is good for him) he can dominate the world and actually kill a few civs before they even meet eachother. A few stratgies to try:
Play a Terra map, take your first warrior and settler and send them exploring into the ocean, in search of that other continent, you know, the one that is void of all other civs. Yea, it's really easy to get a culture victory when you can play the game with literally no army.
Play Continents/Small Continents, like above you can go exploring and find a better location to settle, or (my favorite) find another civ, and found your cap as close as possible. that will make taking them over a cinch. If you start the map on a great location, send your second settler into the ocean.
Play Islands/Small Islands. See above.
see where this is going? A lot of people bag on Polynesia for having a warrior UU and crappy UB (Moai are okay i guess but flight for gold? WTH) but the SA is where it's at. Another way to look at them is naval warfare. Your triremes and Galeas can enter the ocean, but the enemy ships cannot. You can hit them. They can't hit you.
Coincidently, Polynesia is my favorite civ because of their SA. My weak spot is addmittedly naval warfare, but when you can cheese your enemies like that, hehe..
EDIT: Okay, their UU is good for upgrading because of that nifty Haka Dance (enemy -10%), but come one, it's a warrior. ONLY good for upgrading. Just thinking of a Great War Infantry doing the Haka dance in the middle of combat just tickles me pink.