Don't get too excited, but "Benjamin Cocke" was a popular name among both main branches of Cockes who lived along the James River in early Virginia. Many Cockes from both lines migrated to TN/KY, then on to Texas between Mexican War and Civil War. My gggggrandma was Elizabeth Cocke (likely daughter of Thomas, sister of Colin) who married Edward Bland (son of Richard Bland II) and had an uncle and cousins named Benjamin Cocke. Among all Cockes, the name Benjamin likely is sourced in many intermarriages with the family of Benjamin Harrison (the President). Elizabeth's grandson, Colin Bland (aka Colin de Bland) was in the Mex War and settled in Fort Bend Co TX in 1840's and "disappeared" around 1853, perhaps in a flood (or perhaps murdered?). Elizabeth's nephew Colin Cocke married Sarah Fenn in Fort Bend Co TX in 1845 and was murdered same year by a local cattle (and slave) baron who was after his land. Search for "Collin Cocke" for newspaper accounts of that time. There seems to have been other Cockes there at the time. If you google for both Colins you'll see that both had reputations as "hot heads."
Perhaps double cousins to me and both Colins, were sisters Ann Augusta Bland and Rebecca Bland who married brothers Stephen Frederick Cocke and Thomas Robert Cocke. These Cocke brothers were born in KY (their parents had migrated there from VA), went back to VA for college, met and married Bland girls in VA, then the two couples migrated to Victoria, Fort Bend Co before 1850. A third sister, Margaret Emma ("Emma"), married George Harrison in Fort Bend Co. This Harrison was also likely a "Cocke cousin" as he was descended from Benjamin. These Cockes may be from the other branch from my Colin, but, like I said, both branches used the name Benjamin--because both intermarried with Harrisons.
Just thought I'd give you a taste of the loads of Cockes in VA, KY, TN, TX. If your Benjamin is from either line of the VA Cockes, it may be easier to track forward rather than backward. Let me know if you'd like more detail. Happy hunting to you, Cousins.