Eric, thanks for the suggestion again. I inserted a png file Export command in place of the Pause as shown below and it just works fine and shows each and every step now. Probably the png Export requires the output of the updated Graphics3D object a enforcing it to wait until the graphics update is finished internally, or it simply took just enough time :).

a = Graphics3D[{}];
Dynamic[a]
For[i = 1, i <= 20, i++, b = RandomReal[{-1, 1}, {10000, 3}];
 TextStr = {Text["i=" <> ToString[i], {0, 0, 5}]};
 b3g = Map[Sphere[#, 1] &, b];
 a = Graphics3D[{TextStr, b3g}, 
   PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}];
 Export["D:\\Downloads\\a" <> ToString[i] <> ".png", a]
 ]

I would expect that Dynamic is given lower priority for computation time compare to the "main thread". So I think this approach is generally doomed to fail.

I wanted to check each and every single cycle result real time on screen as the calculation goes on

I guess I still don't understand enough of your context. If the computations are going at "machine speed" with no pauses, then how could you even mentally process what you're seeing if you monitor the computations "in real time"?

If you want to inspect every step of the computation, your best bet is to save them and then review them after the computation is complete. If you want to watch things progress as the computation is happening, then I think you're going to need some pauses.

Probably Monitor would be better than Dynamic, but I don't think you'll be able to avoid using pauses. If you're adamant about no pauses, you could insert a dialog, maybe something like this:

For[i = 1, i <= 2, i++, b = RandomReal[{-1, 1}, {10000, 3}];
 TextStr = {Text["i=" <> ToString[i], {0, 0, 5}]};
 b3g = Map[Sphere[#, 1] &, b];
 ChoiceDialog[
  Graphics3D[{TextStr, b3g}, 
   PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}]];]

But I'm not really familiar with the best monitoring/debugging techniques, so hopefully someone else will jump in. I'm also not sure I understand what you really need, so if there's more info/context you can provide, maybe that would help.

You could do something like this instead:

centers = RandomReal[{-1, 1}, {20, 3}];
spheres = MapIndexed[
   Graphics3D[{Text["i=" <> ToString[#2[[1]]], {0, 0, 5}], 
      Sphere[#1]}, PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}] &, 
   centers];
ListAnimate[spheres]