Let the three sides of a triangle ABC be given by the vectors $$2\hat{i} - \hat{j} + \hat{k}$$, $$\hat{i} - 3\hat{j} - 5\hat{k}$$ and $$3\hat{i} - 4\hat{j} - 4\hat{k}$$. Let G be the centroid of the triangle ABC. Then $$6\left(|\vec{AG}|^2 + |\vec{BG}|^2 + |\vec{CG}|^2\right)$$ is equal to ______.