For a structure (usually a tower) that is perpendicular to the ground, if the center of gravity were to go a distance over its base, it will fall over. Can be seen in the leaning tower of piza. The reason it has not fallen over is because its center of gravity has not exceeded the length of its base.
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In both cases, because of their symmetry, the center of gravity is in the geometric center.
If the cube is uniform ( ie it has uniform density) then the geometric center of the cube is its center of gravity.
Everything around you that has mass is an example of center gravity. :)
The center of gravity of a triangle is its centroid. The centroid of a triangle is the intersection of the three medians.
Just about where the center of the hole is.