I create a 3D ball according to this tutorial
https://www.youtube.com/watch?v=39mJPLl-nno
or
https://www.youtube.com/watch?v=3_Kw10dDKkY

Then, I group the whole ball and create hundreds of the same ball by Titled Clone.

Now I need to change the base color of some balls within the network. To do so, I have to ungroup each the ball and select the base circle and change its color. I wonder if there is any trick to quickly change the color of individual balls?

Maybe the trace feature can be helpful?
http://tavmjong.free.fr/INKSCAPE/MANUAL ... Trace.html

What happens if you unlinkthe copies from the original? Will it then let you chg the color?
I really don't like working with tiled clones to be honest, I always get screwed up. I would probably do one color, then duplicate it onto a separate layers, and change the color of the entire thing.

Create your original ball from two circles, one on top of the other. While constructing, set the lower one to a typical base colour. Use a transparent to black gradient on the top circle to let the lower colour show through, giving a similar 3D effect.

The trick now is to unset the fill of the lower circle (it'll appear as black), then group everything together. Create your clones and you'll be able to set the fill on each one individually.

See part 30 of my tutorial series for more details about unset fills and clones: viewtopic.php?f=6&t=11981