I know I've heard this here before but what case is the .257 Roberts based on?

Also, what are the rounds that are based on the .308?

I believe the roberts was based on the 7x57 Mauser

308 I think is just a cut down '06

Yes, the 257 Roberts is based on the 7mm Mauser. The cartridges based on the 308 that are in commercial production are the 243 Win, 260 Rem, 7mm-08 Rem, and 358 Win. If you get into wildcats there are a few more.