I have to admit this has been a bit of a difficult tree to race. There are two Luther Cains born in the 1920's and two Luther Cains born in the 1890s.
Luther B. Cain, born 1920, died 1998, appears to be son of Martin Luther Cain, b. 19 November 1898 and died 1982, and his wife Linnie Mae Miller (died 1957).
Luther Cain, born 16 March 1925 and died 29 March 1982 (Atlanta, GA), would appear to be the son of Luther Cain, born 1 July 1895 and died 17 May 1960, and wife Lydia Graham (they were married 25 February 1924 according to Shelby County, TN marriage records). I found Lydia and Luther in 1930 census of Shelby County, but no children listed. I'm going to try and get down to the TN State Archives next week (I live in Nashville) and pull the obit for the Luther Cain died 1960 to see if it lists any children. According to TN Death Certificates that I found online, Luther (1895-1960) was son of Dennis CAIN and Mary SIDNEY. He is buried in Memphis National Cemetery.