I see a number of family trees on Ancestry that name Joseph Cole and Ruth Sampson as Levi's parents. If Levi was born in 1780, Ruth Sampson Cole is not his mother--she died in 1776 in Plympton, MA.
The Descendants of James Cole of Plymouth lists Levi as a son of Joseph and Ruth. However, I believe E.B. Cole's list is incorrect. In Vital Records of Plympton, Levi is not one of the children listed for Joseph and Ruth.
--Pam Thompson,
Updating and revising The Descendants of James Cole of Plymouth