Born in Cascade, Iowa, Cooke attended the common schools, the local academy, and the high school at Dubuque. He studied law at Dubuque and in the law department of Columbian University (now George Washington University), Washington, D.C., and was graduated from that institution in 1873.
Cooke's educational background was shaped by his attendance at various institutions in Iowa and Dubuque, including local schools, an academy, and high school. He also studied law at Dubuque and Columbian University (now George Washington University) in Washington, D.C., graduating in 1873.