The soundtrack seems to belong to several different genres.
I like Alex North's music for this epic film, but many of the tracks don't seem to fit the Sword & Sandal Ancient Roman mood at all.
The title theme sounds like it comes from one of those big 1960s WW2 epics like Battle of the Bulge.
https://www.youtube.com/watch?v=SxeUnHfzPAo
This training montage from Spartacus' camp on Mt. Vesuvius sounds like a theme from a 1960s Western such as The Magnificent Seven.
https://www.youtube.com/watch?v=UXdF3YFC-7o