It’s a Giant TCX SLR 2015.
I’m not going near replacing outer cabling. I’ll let a bike shop have fun with that. I was hoping the inner would be straight forward if the original outer stays in place. It’s only a couple of months (200 miles) old.
I have the same bike and (had) the same problem, yes you can just thread a new inner through BUT you will need to replace the outer too. I was expecting to be throwing the bike through the window, but it turned out to be the easiest job! My advice, pull the older outer out of the frame leaving the old inner in place as a guide, thread a new outer (you’ll have to remove the rubber grommets in the frame) I didn’t bother replacing the bit of cable under the handlebar tape, my bike has the jagwire adjusters so only replaced the outer up to there. Remove old inner, and put new inner in. Hey presto, one functioning back brake again!
Hope that makes sense!