Brazen Brass on a Chaos Black undercoat, followed by a wash of Gryphonne Sepia.
A couple of drybrushings of Shining Gold, Gryphonne Sepia, and a light drybrush of mithril silver, for that extra shine.
Mine turned out more gold/brass, rather than bronze though.
If you apply a wash to your cannon you might want to let it dry upside down, or facing upwards, or else the wash will just end up at the bottom of the barrel.