And unlike radio, there are ways of catching someone at it.

Not that this would have any effect. It's a lot easier to monitor a few hundred individuals' communications (especially wireless) than it is to tap a big fat trunk line with millions of users and try to spot anything useful.

185 million isnt enough (IMO) to run a cable large enough to handle all their communications, safely all the way across the ocean. And it could be tapped into before it ever even went online, making it harder to detect any power fluctuations. Assuming that they use fiber optics as the poster below, chicago guy, mentions.

One would think the cable would be fiber. While fiber can be tapped. The cable operator can see the fiber and tell how long it is and every tap (splice) on the entire length shows up on a OTDR. If it is wire the wire can be tapped without touching the cable. Fiber is the most secure and for a budget of 185M it will be used.

If someone taps into it, the received light will be less. That will be detected.
They know how much light goes in. They know the loss of the fiber. They know how much light should be on the receiving end. As soon as the light level drops, they will know someone is messing with the cable, or there is a problem that needs to be looked at.

Edited to add:
And if they don't do the tap correctly, they will be able to tell with in reason where the tap is.

also, how do they propose keeping the path of a super long cable secret?

Unless they can constantly physically monitor the cable it won't provide much security.

Where there's a will, there's a way.

during the Cold War. This is old but effective technology.

yup

http://en.wikipedia.org/wiki/Operation_Ivy_Bells

During the Cold War, the United States wanted to learn more about Soviet submarine and missile technology, specifically ICBM test and nuclear first strike capability.

In the early 1970s the U.S. government learned of the existence of an undersea communications cable in the Sea of Okhotsk, which connected the major Soviet Pacific Fleet naval base at Petropavlovsk on the Kamchatka Peninsula to the Soviet Pacific Fleet's mainland headquarters at Vladivostok.[2]:172 At the time, the Sea of Okhotsk was claimed by the Soviet Union as territorial waters, and was strictly off limits to foreign vessels, and the Soviet Navy had installed a network of sound detection devices along the seabed to detect intruders. The area also saw numerous surface and subsurface naval exercises. More at link

'cause they do it too!