We have about six cubicles up against a wall in an office building. I am taking the 2 on one end apart but the first one has the power fed into it from the base of the wall from a hard wired box. Since I'm taking the first 2 stations apart,the electrical cable will not be long enough to reach to keep the other ones powered. Can I extend this cable in any way or do I have to get a longer one and wire it into the box on the base of the wall?

It is not that simple. First, changing the design of the cubicle may cause a code violation. Certainly, it would be a product design problem.

Are all of the cubicles being connect to the same branch-circuit? Is the branch-circuit a 15 or 20 amp branch-circuit?

Can the branch circuit carry the load of these cubicles? From your description it seems as though you already had these cubicles installed and working, is that true?

If you're located in the United State it's likely that you are not legally permitted to do electrical work unless you are
appropriately licensed. The liability involved here is not trivial.
Why not hire a licensed electrician and let him decide how best to approach this...

I agree with hfcarson. This sounds like a very simple task. If you have to ask how to do it you are not qualified to do it and most likely not permitted to do it.

Can I extend this cable in any way or do I have to get a longer one and wire it into the box on the base of the wall?It's actually very easy. Just get on the phone and call a qualified electrician. He'll make quick work of it.