I make a glassy ball by drawing a base color circle. Then, add several layers with gradient, smaller white ellipse, etc.

Is it possible to save all of these extra layers as a pattern/effect to quickly add them to a color circle to generate a glassy ball?

I have to draw many glassy balls. I am looking for a shortcut to quickly add glassy effect to a circle.

So you want to make different colors circles, and than apply some kind of object on top of it, to make it look both like a sphere and glassy? That's exactly what Inkscape filters do. I don't know if there's one that will give an object both the appearance of being a sphere, and the appearance of being glassy (like a marble, I guess?). But you certainly can look at the filters, and maybe there is one already.

Or there are other ways to approach this. After you draw all the various objects, you could:

-- group them together, and duplicate or clone the group, and manually position it on the new circles
-- convert it to a pattern, and draw a 2nd circle on top of the colored circle, and apply the pattern to it (might have to adjust the pattern to fit the circle)

Or if you know how (or willing to learn), you could try to create your own custom filter using the Filter Editor. And we finally have a tutorial for making new filters: http://tavmjong.free.fr/blog/?m=201509 (Part 1 is underneath Part 2, for some reason)

It would also be possible to do this with an extension, I think - that would create new objects, instead of using filtering. Can you show us an example of your glossy circles?