Finding surface area of 3-dimensional figure

I have plotted a 3d figure of a cube with 8 spheres cut out of the corners. I want to find the surface area of the object. Is there a way to do it without calculating the surface area of an 1/8 of a sphere and finding the surface area of a squere...etc ? Please help ASAP. I wanted to count the pixels on the surface, but I am not sure if that is possible.

[Walter Roberson]

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