Tested on Python3.6 on Ubuntu 18.04
The following code snippet produces the wrong results.

Snippet:

M = [[[0] * 2] * 2] * 2                                                                
M[0][0][0] = 1                                                                                                                                                                 
print(M[0][0][0]) # Should be one                                                                      
print(M[1][0][0]) # Should still be zero 

My output:
1
1

For some reason when you assign to any list inside the 3D matrix, all lists in the array are changed, 2D Matrix works but 3D modifies every 2D matrix.

In Python, multiplication on a list does not make copies of the values in the original list.  So what you have done is equivalent to the following:

  a = [0, 0]
  b = [a, a]
  M = [b, b]

Hence:

  >>> M[0] is M[1]
  True
  >>> M[0][0] is M[0][1]
  True
  >>> M[1][0] is M[1][1]
  True
  >>> M[0][0] is M[1][0]
  True

So the following *all* modify the first value in "a":

  M[0][0][0] = 1
  M[1][0][0] = 1
  M[0][1][0] = 1
  M[1][1][0] = 1

That is why you are seeing the result you reported.  Depending on your needs, better solutions include using a list comprehension, spelling out the for loops (for readability), a helper function (for complex problems), or simply spelling out the full list literal instead of composing it.  Regardless, I highly recommend using a solution that is easy for a new reader to understand.  Even if no one else will read this code, your six-months-from-now self will thank you. :)