I have a 3d box with the predetermined color and it looks like this:
When I change the color, for example, to red, know it looks like this:
So as seen, now all the faces have the same color intensity and it is not possible to distinguish the edges. Is it possible to look as in the first image with different color?
This is how I do it:
Inkscape is a 2D tool, and it is not able to manage 3D objects. The Box Tool simulates a 3D box by creating 6 plain faces with the expected proportions:
Usually only 3 faces are visible, but the box is like a group of paths, and if we ungroup it (Ctrl+Shift+G), we can see all the faces, each with a different shade of blue (please note that after ungrouping a box you can no more re-group it and apply the Box Tool):
The Box Tool doesn't provide a way to change globally the colors maintaining different shades, and if you apply a color on the box (remember, it's a group of paths), it fills all the 6 faces, like in your example.
The way provided to accomplish to your task is described here:
If in Inkscape preferences for 3D Box the Last used style option is selected, the next box will be drawn with the last fill and stroke used:
The 3Dness of your shape is not essential here. You have three separate objects, maybe grouped, and you want to keep their lightnesses and color saturations, but change the color hue.
Extension Color > HSL Adjust is for this job. You give new hue. You can also adjust relative lightness and relative saturation (=plusminus percentages)
You probably must adjust all sliders for best appearance because RGB color system isn't designed to be subjectively linear like CIELAB or its polar version HCL. You can see that with same saturation different hues look differently "colorful". In RGB the goal has been streamlined computing without too heavy math. Inkscape has only RGB.
Another possibility is to make the faces without color, let them have only different greyshades. Make a duplicate of the shape (=Ctrl+D). It settles automatically on the top. Combine the faces of the duplicate with Path > Union. Let it have blending mode "Overlay". You find it in the Objects panel. Give the wanted color to the top object. To change the color you recolor only the top object. It can be made by copying a good color from elsewhere with the color picker. If you use extension HSL Adjust, new color must be typed as number.
Here's an example with blending mode Overlay:
top left: A three part shape
top right: the union of the parts, colored to blue
bottom left: union is placed on the original version, blending mode = Overlay
bottom right: parts moved a little apart
It works also from the shaded parts to solid color. Here the colored union is in the bottom and the grey parts have blending mode luminosity:
Actually the 3 part shape can have also other color than grey. Only the luminosity is taken into the account.
BTW. Blending modes create color mixes between the topmost object and what's below it The all have own mixing formula. Modes Multiply, Hard light and Color can be as useful. One must do plenty of tests to learn how they work. Their math is presented in the documentation.
