That might be a better alternative.
'Cubic light years'... Hm. I'll think on that between now and my next post.
How does this compromise work for everyone?
The Constitution was a proven design, as all but two of the original 2240s production line were still in service, and during their careers had increased the volume of known space by thousands of cubic light years, adding detailed maps of hundreds of sectors to Federation star charts.
One single sector (again assuming a side length of 20 light years) would already contain 8000 cubic light years, so the two numbers you gave don't exactly match. Replace "thousands" with "millions", and I think you're good to go.
Other than that, keep the chapters coming!