Cobham participated in Maj. Gen. William T. Sherman's Atlanta Campaign. He took command of 3rd Brigade, 2nd Division, XX Corps, when its commander, Col. David Ireland, was wounded at the Battle of Resaca on May 15, 1864. He led the brigade until Ireland returned on June 6. Col. Cobham was killed while leading his regiment at the Battle of Peachtree Creek on July 20. Cobham was awarded a posthumous brevet promotion to the rank of brigadier general on July 19, 1864, predated to before his death. Geary, his division commander, described Cobham in one of his letters as a valuable and beloved officer.