According to Bruce Warren, we see some evidence for the name "Shule" (Ether 7:7) in Mesoamerica. The name Xul (pronounced "Shule") was an important name in the Mesoamerican calendar. It is the name of the sixteenth day of the 260-day calendar of the Yucatec Maya. [Bruce W. Warren, Blaine M. Yorgason, Harold Brown, New Evidences of Christ in Mesoamerica, Unpublished Manuscript]
“Nevertheless Kib Begat Shule in His Old Age”
According to Matthew Brown, inasmuch as the Jaredites supposedly came from the tower of Babel, and one of their kings was named "Shule" (Ether 7:7), it is interesting to note that Shulgi is attested as the name of a king who reigned in Sumeria from 2094-2045 B.C. (see E. Jan Wilson, "Inside a Sumerian Temple: The Ekishnugal at Ur," in Donald W. Parry and Stephen D. Ricks, eds., The Temple in Time and Eternity [Provo, Utah: Foundation for Ancient Research and Mormon Studies, 1999], 319. [Matthew B. Brown, All Things Restored: Confirming the Authenticity of LDS Beliefs, p. 213]