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The global and semi-global analytic hypoellipticity on the torus is provedfor two classes of sums of squares operators, introduced in "AnalyticHypoellipticity for Sums of Squares and the Treves Conjecture" by P. Albano andA. Bove and M. Mughetti, and in "Analytic Hypoellipticity for Sums of Squaresand the Treves Conjecture. II" by A. Bove and M. Mughetti, satisfying theH\"ormander condition and which fail to be neither locally nor microlocallyanalytic hypoelliptic.

(Semi-)Global Analytic Hypoellipticity for a class of "sums of squares" which fail to be locally analytic hypoelliptic