Definition for center of gravity is the point where weight of the object balance in all direction. Finding the CG for any irregular shape or regular shape whether it is a rod or rock is all the same. You may hang the object at different angle, note the rope line drawn across the object. There will be only one cross over point of all the hanging line in all direction. That point is the CG of such object.
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Each body has its own centre of gravity. The centre of gravity of two regular shapes - an equilateral triangle and a square will be different so why should the cog of a regular and an irregular shape not be different?
The center of gravity of an irregular shape can be measured, for example by hanging the object from two different points (points of the object), then watching where the lines (from the point where it is hung up downwards) intersect.If you know details about the shape, the center of gravity can also be calculated by integration. Basically this means dividing (through calculation) the shape into small pieces, and adding up the results.
Sorry but you need to be a little more clear next time
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.