Steve,

I looked into this several years ago when the following appeared in some publication (I do not know recall which one):

“Sherman and Boyd, another original faculty member of the precursor to LSU, were good friends, [David] Madden said, a relationship fostered by their mutual love of classic literature. Sherman sent Boyd a cannon from the ship of Union Adm. David Farragut. It now sits outside LSU’s military science building, Madden said.”

The two pieces in question are:
Ames Foundry, Registry #7, Inspected by GTB, 1861, weight 924 lbs. [George Thatcher Balch]
Ames Foundry, Registry #9, Inspected by GTB, 1861, weight 920 lbs.

While it is true that Sherman and Boyd were friends and that Sherman sent some rifles to the cadets, he did not provide those two cannon. The following paragraphs are summarized or quoted from Warren Ripley's book:

Charles Tillinghast James of Rhode Island developed several artillery projectiles as well as a 14-pounder rifle. The two rifles at LSU are a type designated by Civil War artillery experts as a 3.80-inch bronze field rifle, James Type 2, Series 3.

“The weapon, normally bronze although a few were made of steel, is found in most of the field-gun parks and two excellent specimens grace the entrance to the science building at Louisiana State University at Baton Rouge. Bores measure 3.8 inches rifled with 10 lands and grooves (an occasional piece will be found with 7), and length overall is 73 inches. Both are marked on the right trunnion ‘Ames Co., Founders, Chicopee, Mass.,’ on the left ‘1861,’ and on the muzzle face, ‘GTB.’

“Accompanying historical plaques28 state they fired at Fort Sumter and were presented to the University after the war by General W. T. Sherman. The latter part of the statement is doubtful, and the former certainly is not borne out by fact....” (pp. 169-70)

“28. The author is indebted to Lt. Col. Arthur V. Crego of The Louisiana State University for a majority of information on the weapons. Col. Crego dug out available records in the Baton Rouge area and found they fail to link the cannon with either Fort Sumter or Gen. Sherman. He attributes the basis of the plaques largely to legend.” (p. 187)
Warren Ripley, "Artillery and Ammunition of the Civil War" (Charleston, S. C.: The Battery Press, 1984)