Richard M. Cox was born around 1830 in Charlottesville, Virginia. He was married from the fall of 1849 to the fall of 1850 to an unnamed woman. He married his second wife, Elizabeth Cox, on November 11, 1855, in Pike County, Ohio. Together they had an unnamed child who died in infancy. Cox worked as a farmer before the war and enlisted in the Union army as a free man.  

Cox enlisted and mustered in as a corporal at the age of 34 on January 9, 1864, in New Haven, Connecticut. His service record describes him as 5 feet, 10 3/4 inches tall, with black hair, black eyes, and yellow complexion. He served in Company K of the 29th Connecticut Volunteer Infantry Regiment with Jesse Cowles, also of Albemarle County. He received a promotion to sergeant very soon after he enlisted in January 1864, but he was reduced to corporal on March 1 and to private on May 1, 1865. Cox was absent while sick in a field hospital for some time but presumably returned to duty to march through Richmond with the 29th Connecticut when the city was captured. He mustered out with the 29th Connecticut on October 24, 1865, in Brownsville, Texas.

Cox likely returned to Ohio following the war. He re-enlisted in the army on March 14, 1867, and was promoted to sergeant on March 14, 1870. He served in Company E of the 41st US Infantry Regiment before it was consolidated with several other Black regiments into the 24th US Infantry Regiment, after which he was attached to Company I. His Black regiment, known as the "Buffalo Soldiers," served in the West after the Civil War.  He died on April 24, 1874, in an unknown location of unknown causes. Following his death, his widow Elizabeth began receiving a pension of $8 a month on July 21, 1890. According to her pension, she died on March 4, 1893.