All shadows are coloured, but that depends on the lighting source.
Natural shadows appear blueish in tone because the natural light is blocked from the shadow area, leaving only indirect light (refracted) and blue light from other parts of the sky.
By playing around in a controlled setting with different coloured light sources will create different coloured shadows.
* Colored light is just light that has been filtered in some way.
* Most of the filtered light we are used to is light that is reflected off a surface.
* The surface absorbs some of the light and reflects the rest. This effectively filters it.
* The other way we see filtered light is when light passes through a substance.
* The substance absorbs some of it and lets the rest pass through again acting as a filter.
* This creates what OP is calling “colored shadows”.
* For example a red stained glass window.
* White light hits the glass and all the colors except red are absorbed by the glass.
* So some red light reflects off the glass but also some red light passes through the back of it.
* It looks like it casts a shadow because it’s the same shape and position that an actual shadow would have but it’s not a shadow because it’s made of light instead of the absence of light.
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