Get some tape and mark each wire, so you can tell which of the fourteen wires are which. Then get a cheap multimeter, like from Radio Shack, and start taking resistance measurements between the wires, making a chart for each of the three cables. If the white wires are the commons, then the resistance from the other colors to white will be about the same, and the resistance from one of the other colors to another 'other' color will be about double.
It is customary to make the white wire(s) the common, because most any multi-conductor cable will have a white wire in it.
You may have three separate locations for the sprinkler valves, which would account for the three cables. Or, it might be that one valve location has more than six valves, and the installer used two multi-conductor cables to feed it.