The phrase 'cable has been damaged' is correct and usable in written English.
Example Sentence: I just realized the cable has been damaged, so I'll need to get it replaced.
PCCW, Hong Kong's main fixed-line telecommunications provider, said that several of its partly owned submarine cables had been damaged.
This webpage talks about the efforts and challenges involved in laying underwater cables on seabed floors around the world, incidents in which those cables have been damaged or cut, and how government agencies, like the NSA, have tapped into such cables to aid in its spying efforts.
Because the electrical cables had been damaged, Cedar Point employees had to manually bring down the gondola.
The operator said that four of the eight cables in the interconnector had been damaged, reducing its capacity from 2,000MW to 1,000MW until February next year.
Mr. Burke of Con Edison said a number of 13,000-volt feeder cables for the utility's electric system had been damaged in the explosion.
After opening up the case, unplugging and replugging in cables, it turned out my power supply had been damaged in some way.
