storage capacity

i have 8 gb 3rd generation nano. ipod says my files are full, it shows i have used 5.79 (1421 songs) if my math formula is correct a 8 gb should have 7.45.
i have no art work, no videos, no art work no anything but music, does the itune software take up 1.66? it seems a lot but the Ipod world is fairly new to me. so new that when you advertise up to 2000 songs for an 8gb i believed that was what i was buying or at least close to it.

thanks,

The 2,000 songs statement was made under the assumption that all songs will average four minutes in length. It is likely that a lot of your music exceeds four minutes in length.
As for your system, in my experience, it will take up aproximately half a GB of disk space.