The book "Field Artillery Weapons of the Civil War" by Hazlett, Olmstead and Parks, mentions a iron 3" rifled cannon built by Noble Brothers of Rome, Georgia, on page 60-61 and appendix 6B on page 244. Eighteen of these guns were made in 1861 and the final four in 1862. Information of these guns is lacking because of confusing records but mention is made of guns made for the Jeff Davis Artillery of Alabama and Bondurant's Battery but this is not reliable

The book "Confederate Cannon Foudries" by Daniel & Gunter lists five of these guns being turned in to the Augusta Arsenal in 1863 and being melted down for new models. The orginial contract, signed in 1861, of the Noble Bros Foundry was for 27 of these iron rifled field pieces. The Cherokee Artillery of Rome Georgia was issued three 6 pounder smoothbore and three 3" rifles all made by Noble Bros. Most of the production went to Virginia with Cutt's Georgia Battery and Griffin's Virginia battery being armed with Noble cannon. The quality of the castings of these guns by Noble was reported as good. Two of these guns went to Savannah and one to Calhoun Georgia. Transportation of raw materials caused difficulties and delays in production. A shortage of labor also contributed to the problems and delays of production. Production of cannon was halted at the foundry after a argument about poor casting of guns in November 1862.

The National Registry of Surviving Civil War Cannon, compiled by Wayne Stark (now deceased) lists your gun on page 13 as being in the Centennial Park of Naperville Illinois. It has a rifled barrel of 12 left-hand twists which is not confirmed data.

Hope this helps.
Ron