You can find August Mullen in Volume I of the Report of the Adjutant General of the State of Kentucky Civil War.
Kirk Jenkins recently published The Battle Rages Higher: The Union's Fifteenth Kentucky Infantry (Lexington: University Press of Kentucky, 2003) contains a roster and indicates August R. Mullen was born in Shelby county, Ky and was a 20-year-old clerk when he enlisted. He was 5"9" tall , with a light complexion, blue eyes and light hair. Pvt. Mullen was wounded on Oct. 8, 1862 at the battle of Perryville and also near Dallas, Ga. on May 29, 1864. I recommend the book highly.

A brief history of the 15th KY. can be found at the Capt, Thomas Speed's The Union Regiments of Kentucky web site.