Hi Frank,
I think I may have seen this query before and somehow overlooked it; sorry.
I used to solder my cables, but have since found beta-cyanoacrylate "Super- Super Glue" (the kind that advertises on the package that it works with a wider range of items, including flexible materials and leather) does the job better for me than solder. The primary advantage is you don't need a soldering iron and can re-do it in the field. Best of all, this kind of super glue has very good "wetting" characteristics when fresh and flows well into the cable strands, gluing them together from inside without leaving a small blob on the outside that can sometimes be problematic when feeding the cables. If you don't want to wait for the super glue to dry, you can add water (or spit) as an accelerator.
I carry a tube in my underseat bag on day rides and tours, so it is always handy for securing the ends of field-cut cables. Just as in hospital A&E (Emergency) rooms, I've found this kind of super glue also makes a dandy substitute for field sutures, and can be managed one-handed much better than needle and thread. If one runs out of patches, a single drop placed in a tube hole will fix a flat almost indefinitely and has actually replaced patches for some of my use. Does a great job fixing glass-caused tread slits also.
Here's the steps I use to solder a stainless-steel cable:
1) Cut the cable cleanly with a sharp pair of v-jaw cutters (Dremel cut-off wheels leave emery dust behind). My SunTour v-jaw cable cutters are for cables, not housing, and are very sharp. I use my Felco heavy-duty v-jaw bypass cutters for housing, which they go through like butter.
2) Make sure it is clean and free of grease. I polish with plain steel wool, then wipe with xylene while wearing gloves.
3) I use Harris Stay-Clean (acid) or Kesler 817 Stainless Steel flux; brush on or dip the cable end in it.
4) Using a 100-200 watt soldering iron, get the wire hot enough so it (the wire) melts the solder on contact (I use Kester 98% tin, 2% cored silver solder).
5) Wipe off excess solder with a damp tissue as you slide the iron tip toward the end of the cable.
6) Wipe off and/or neutralize (baking soda) any remaining acid flux -- this includes the cable and the iron tip -- to prevent corrosion.
7) Final clean with xylene or polish with plain steel wool.
Beta-cyanoacrylate is much easier and quicker.
I hope this helps.
Best,
Dan.