200 cubed is way more then 8,000. One sector is 20 x 20 x 20 and that is 8,000 cubic light years.
Picard says something to the effect that the Federation stretched across 8,000 light years, which doesn't necessarily mean it is a perfect sphere with an 8,000 light year diameter but could just be the furthest distance between two Federation systems.
Hmmm, your right... miscalc lol. I should make a seperate discussion about that. I highly doubt the Federation was 8,000 light years in diameter. That would take a ship (in Voyager's terms) 8 years to travel from one border to the other... that seems just too far and it would be impossible to mobilize so many ships and bring them to the front lines if it was that large. I always thought picard was speaking in some volume or area terminology since it says "spread accross" which is left open to interpretation. But DS9 and TNG favor a smaller Federation model. The USS Valiant's mission was to circumnavigate the Federation in 3 months.... yeah 8,000 light years just to go through it? I doubt it.