In the case there are no limitation on the way we sort the different values (i.e. it's not a normal dice which opposite sides sum up to 7), and there's also no rotation allowed (the cube is fixed) - then the answer would be 6! = 720 options.
(n-Factorial is the number of different unique combinations you can arrange all the numbers 1,...,n in a series)
Now let's consider 1-axis rotation is allowed.
You can choose 6 values for the upside face, then you would be left with 5 values for the downside face. Sorting out the 4 faces of the sides would normally be 4! but since you're allowing rotation, this needs to be divided by 4, since each no-rotation combination is equivalent to 4 with-rotation combinations (1234 = 2341 = 3412 = 4123).
So the answer would be 6!/4 = 6*5*4!/4 = 180.
(Note that it does matter here which value you choose for the upper and for the lower, since if you turn them around, the dices will not be the same - but will switch between clockwise, or counter-clockwise, is. a dice with 6 on the top, 5 on the bottom, and 1234 on the sides, is different than a dice with 5 on the top, 6 on the bottom and 1234 on the sides)
Now let's consider 2-axis rotation is allowed.
We would need to take our last answer, and then divide it to take into account that now we're allowed to "play" even more with the dice. We now find out that each "unique" combination in the 1-axis version is equivalent to 6 different combinations in the 2-axis version. 6,1234,5 = 5,4321,6 = 1,5264,3 = 3,4625,1 = 2,5361,4 = 4,1635,2 (the notation I'm using is upper,4-sides,lower).
So our answer will be 6!/4/6 = 6*5*(4!/4)/6 = 30.
Now what would be the answer in the case we limit ourselves to normal dices, i.e. dices that follow the pattern that each opposite sides sum must be equal to 7?
This means that we can now only freely choose 3 faces of the dice, corresponding to its 3 dimensions space, since choosing one face number to be equal to a value, immediately sets the value of the opposite side.
So for no rotation - we could choose 6 values for the upper side, but then immediately the lower side is set, so you can choose 4 value for a another face, but then the opposite face is again set, and finally you can choose 2 values for the next face, which will immediately set the final face. I.e. the answer is 6*4*2 = 48.
For 1-axis rotation - we saw that we need to divide by 4: 48/4 = 12.
For 2-axis rotation - we need to further divide by 6: 12/6 = 2.
And that actually corresponds with the two normal 6-sided dices that exist in the world, called: clockwise (Also - left handed), and counter-clockwise (Also - right handed).