SScala, my hunch is that while I mention "cable" as "the steel cable", others mean "cable" as "the entire cable&sheath assembly"...
...see JOG's and Verslagen's suggestions.

Verslagen says "The cables are held in place by a couple of cable ties.  pull a tab and they pop loose, thread the new cable in..."
I believe he's actually speaking about the cable sheath.

Two weeks ago I snapped the clutch cable (see thread "I had to McGyver it") and I simply pulled the snapped cable out and fed the new cable in... through the sheath , from handlebars to clutch lever.

In your first post you mentioned a brake cable, so I assumed you meant the rear brake.
If it's the front brake you are talking about, may I suggest you:
- recondition the brake hydraulic pump (it's just a wipe of the piston and fitting new seals),
- recondition the brake caliper,
- fit steel braided brale line cut to proper length (don't forget to allow for suspension travel in compression and in elongation!)

As for the clutch, I stand by my words, 35 years of replacing clutch cables have taught me they snap in only three occasions:
- when you're late for work...
- when you're out with the girlfriend/wife...
- when it's raining or after dark...
Or any of the three, combined...

Under these circumstances what you need is a "plug&play fixit", which is exactly what I suggested, a clutch cable already in its sheath and with lugs soldered at both ends.
Just pull away old snapped cable, ignore old sheath (you can deal with it afterwards) clip new lugs clutch side first, handlebar lever next, and you're ready to roll in 60 seconds !