Cochran was born in Webster Groves, Missouri; his father and maternal grandparents were Irish immigrants.[1] He attended the public schools in Webster Groves. He was employed in the editorial department of various St. Louis newspapers for many years, and served as assistant to the election commissioners of St. Louis from 1911 to 1913.
In 1913 Cochran became secretary to Representative William L. Igoe 1913–1917, serving in that capacity again from 1918 to 1921.
Cochran studied law and was admitted to the bar in 1921 at St. Louis, Missouri, but did not engage in extensive practice. From 1921 through 1926 he served as secretary to Representative Harry B. Hawes.
Subsequently, Cochran was nominated by convention and elected to the Seventy-fourth Congress, and reelected to the Seventy-fifth and to the four succeeding Congresses, serving from November 2, 1926, to January 3, 1947.
Cochran served as chairman of the Committee on Expenditures in Executive Departments (Seventy-second through Seventy-sixth Congresses), and the Committee on Accounts (Seventy-sixth through Seventy-ninth Congresses). He was not a candidate for renomination in 1946 to the Eightieth Congress.
Cochran died in St. Louis, Missouri, on March 6, 1947, and was interred in Calvary Cemetery.