Understanding Purcell's Cube: Attraction to Mass Center?

[fluidistic]

In the Spanish second edition of "Electricity and Magnetism", Berkeley Physics Course, volume II, page 27, Purcell states that a cube with a perfectly constant density does not attract external bodies as if its mass was concentrated in its geometrical center.
However he does not say how does such a cube attract other bodies...

The only thing my intuition tells me is that if I am in front of a cube in such a way that I'm closer to a vertex than any other, I will be more attracted by the vertex than any other part of the cube. However I'm not sure it implies that I'm not attracted by the center of mass of the cube.
The comment from Purcell blows up my intuition.

Can you help me to understand, please?

 

[atyy]

A point mass has a gravitational field that is spherically symmetric.

A sphere also has a gravitational field that is spherically symmetric. So if you're outside the sphere and examining the gravitational field, you wouldn't be able to tell if it is the field of a sphere or a point mass.

A cube's gravitational field is not spherically symmetric does not. So if you're outside the cube and examining the gravitational field, you'll be able to tell that it isn't the gravitational field of a point mass.

 

[Naty1]

For some further insights see this thread beginning especially with post # 3:

Newton's law of gravitation,
https://www.physicsforums.com/showthread.php?t=334537

 

[fluidistic]

Thanks a lot to both!