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.
Updating and revising The Descendants of James Cole of Plymouth