Yes it is possible as I was going to do this with mine before I sold my iPhone. You can get an iPhone to USB & Aux cable (see here http://www.amazon.co...g/dp/B002ATMN22)
You would just connect the 3.5mm jack as the other guide suggests; you would then need a USB/car charger adapter (to act as a transformer as USB is 5v) then just plug the usb into this behind the dash.
Hope that makes sense. Haven't actually done this mod as I said I got rid of my iPhone, but I can't see any reason it wouldn't work.
EDIT: Just seen that you didn't want to hardwire the iPhone cable. You could just wire both a USB socket and a 3.5mm socket into your cubby and then plug in the cable I linked above - should work?