You have to understand that there are two considerations regarding the wire size.
The first consideration is the ability of the wire to withstand the current. This is a function of the amps it is carrying and the ambient temperature. The current flowing through the wire heats the wire, and at some point the heat will cause the insulation to melt and bad things happen.
Obviously, the type of insulation on the wire will determine the maximum temperature it will be able to withstand.
A typical maximum capacity, for 16 awg wire in an open ambient (plenty of fresh air to cool it) is 21 amps. This is not enough for the 27 amps that you need.
In most cases you will experience an undesired voltage drop well before you need to worry about the insulation melting. The voltage drop is a function of the size of the wire, the current, and the length of the wire.
If you want those lights to be bright then you will not want any more than a 10% drop in voltage to them, which means instead of 12 volts they will only be getting 10.8. You need to get the positive wire up to the top of the tower and a ground wire back, so I would guess that you would have a run of 20 feet (10 up, 10 back). To keep the voltage drop less than 10% at 27 amps you will need 12 awg wire.
If you want only a 3% drop you will need 8 awg wire.
Here is a good web site with all this information:
http://www.ancorproducts.com/ go to "techinical information" then "Wire Calculator"
You might want to consider grounding the tower (put a big cable to one of the bolts holding the tower to the boat) and use the tower as ground. That will cut out half the run as you will only need to run the plus wire up the tower and not a ground.