I wanted to test Azura Star.

So, today, I made the quest and now I have Azura Star.

Test: As soon as I had it in my inventory I went to kill a Mammoth (soul trapped in a Grand Soul Gem). I killed a second Mammoth (same thing). Killed the Giant (soul trapped in a Great Soul Gem). Azura Star is still empty.

Good. For the moment everything seems ok.

So I went to Whiterun and stored all my Soul Gems in a cupboard except:
One empty Great Soul Gem
One empty Grand Soul Gem.

I returned to kill first the Giant: Soul trapped in the Great Soul Gem.
I killed a Mammoth: Soul trapped in Azura Star!!! So I dropped the Star on the floor and pick it up. I checked to see if it was empty, it was.
I killed the second Mammoth and the soul went trapped in the Grand Soul Gem!

So now, what is wrong with Azura Star?

Sometimes the soul goes into a Grand Soul Gem and sometimes, even if there is an empty Grand Soul Gem, the soul is trapped by Azura Star. No my Azura Star is not black.

Edit: Of course I reloaded as I never killed Mammoths before. I was only testing.

It may not have registered in your inventory if you dropped it and picked it back up again in front of the Mammoth.

Your Azura sounds like it is working as it should.

i heard it depends who you got the azua's star from 1 is the black souls it can capture and 1 can capture white souls here a link for the wikia for the item and ect. http://elderscrolls.wikia.com/wiki/Azura%27s_Star_(Skyrim)

He mentioned Azura Star not The Black Star!
seems odd though, no problems here with my Black Star!

But he only dropped it after the soul went into the wrong gem: Azura's Star instead of an empty Grand Gem.

No. If you read again, you'll realize that first it went in soul gems and not Azura Star. And a few hours later the Giant's soul went trapped by a Great Soul Gem and the Mammoth's soul by Azura Star though there was an empty Soul Gem. In this test, once the soul goes into a gem and once into the Star.. Why?

Yes, exactly. I dropped Azura Star to see if the second soul would go into Azura or the empty gem. It went into the empty gem which is OK. But for the first Mammoth there was no reason for its soul to fill Azura Star. It should have gone also in the empty gem.

A couple of questions:

1) When you first went soul-trapping with Azura's Star, did you have a stack of empty grand soul gems, or one?

2) Have you tried repeating your experiment with 2 empty grand soul gems in your inventory?