Centroid 80

Let $\overline{CG}$ intersects $\overline{AB}$ at $D$ ,then $\overline{DG}=2,\overline{DB}^2=3^2+2^2-2\times3\times2\times\cos60^\circ=7$

So $\overline{BD}^2+\overline{DG}^2-2\overline{BD}\times\overline{DG}\cos\angle BDG=\overline{BG}^2=9$ $\overline{AG}^2=\overline{DA}^2+\overline{DG}^2-2\overline{DA}\times\overline{DG}\cos\angle ADG=\overline{BD}^2+\overline{DG}^2+2\overline{BD}\times\overline{DG}\cos\angle BDG=13$