Depending on the particular box, there are two problems:
Pushing cable in from the outside will end up with a tangled mess.
With some boxes, the output hole isn't just a hole but a plastic piece that "bites" the cable in one direction to prevent it from slipping back into the box.
The solution is to:
Open the box on one side. That will allow you access so that you can pull the cable in and loop it the same way as the rest of the cable to prevent tangles and allow you to pull it out normally in the future.
If there is a plastic piece that "bites", carefully remove it from the box. Depending on how it is designed, you may be able to put it back afterwards. But if you can't put it back, leave a couple of feet of cable out of the box and tie them in a simple knot to prevent the end of the cable from slipping into the box. (That's what cables like to do in the back of the truck when you're not looking.)
Very often it just isn't worth the hassle - if it is < 50 feet then why bother opening up the box, removing the plastic piece, etc. And if it is > 50 feet then do you really want to sit there coiling it up "just so" instead of an easy coil outside the box. But if you do that, use a cable tie instead of tape. You should have cable ties around anyway for securing cables neatly in various places, and that way when you are ready to use the extra cable, just snip the tie open and you're all set - as opposed to dealing with removing the tape and dealing with sticky adhesive on the cable.