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So I basically ask for points of this cube to color according to their distance for the origin. So if the color ramp is black to the white furthest point should be black and the closest one must be white. Is there a way for me to colorize the object this way? I also want to change its location so it needs to be updating its data live. Thanks

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Yes it is possible but I am not entirely sure what exactly are you looking for... you can use a spherical gradient like this and this could be your starting base... use some plane as a reference object while using it on the more complex objects like this cube:

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    $\begingroup$ Hi :). Just to add, you can control the gradient spread and position using the Math > Multiply Add node imgur.com/a/U5vPjxg (click image to play the gif) $\endgroup$ Oct 12, 2021 at 13:11
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Check out the Grading Texture in the shader editor with set to spherical.
For an indipendant center set the Texture Coordinate to Object and use another object as reference.

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