From what I can see & have read, William Columbus Blake's the son of Willington Blake, b. abt 1812 VA & his wife Eliza Smith, b. abt 1815 GA.
Willington is on the 1880 census in Meigs Co., TN, where William C.'s on later censuses. Willington brought the family there from GA, where they're on the 1860 & 70 census, on the 1850 census of Lumpkin Co., which is the same area, & on the 1840 census of Cass Co., GA
There's a Henry W. Blake who's abt the same age as William C. & lives in that same area of Meigs Co., who may be close family, but I haven't been able to tie him in completely.
Some of Willington's family are in Chattanooga, Hamilton Co., TN
Willington's daughter Mary E. Blake, b. 1844 Lumpkin Co., married Benjamin F. Haney in 1859 Dawson Co. This family lived as far south as Atlanta & Marietta, GA, and are in Bradley Co. TN on the 1880 census, I think. Benjamin died in Chattanooga in 1892 & his wife went back to GA & lived with their son & only known child, James H. Haney,b. abt 1865, who himself later moved up to the Chattanooga area, & died abt 1950 or a bit later.
Willington's son, Leroy Martin "Lee" Blake, b. abt 1851, is with wife & children on the 1880 Gwinnett Co. census, then moved to Marietta, Cobb Co., GA, where he lived & raised his family and died there in 1918.
These are the only children of Willington's, other than your William C., that I've got much on, so far, but Willington had many daughters who probably married in Dawson Co., GA or vicinity, so they're hiding behind married names until the marriage records for Blake brides there can be looked at.
I came into this investigation because James H. Haney's wife was Ella Jane Scoggins, a niece of my gr-gr-grandmother, Mary Caroline/Carolyn Scoggins of Marietta.
I'm in the process of working on these families and am putting what I find in my Ancestry tree, where it can be seen.
You can email me at firstname.lastname@example.org if you have questions.