Yeah, you need both of them: plug the 6+2 into the 8 pin female slot on the 780, and just a 6 pin into the 6 pin female on the 780. It sounds like you do have them, what exactly is the problem?
I have a cable like that. 8 pin for psu, then splits into a Y with (2x) 6+2's. it just seems weird though because the second 6+2 is splitting off in the opposite direction and to get it to go the same way as the other 6+2, to connect to the GPU, I have to bend it at quite an angle. And since the cables are sleeved this bend seems kinda sketchy
Don't worry - sometimes the psu makers do that expecting the user to come up (or over) between two cards, rather than needing both connectors on one card. If you have a second cable, use both, that way you won't have to worry about bending the cable.