In class object, how to auto update attributes?

if updating one property due to an update on another property is what you're looking for (instead of recomputing the value of the downstream property on access) use property setters:

class SomeClass(object):
    def __init__(self, n):
        self.list = range(0, n)

    @property
    def list(self):
        return self._list
    @list.setter
    def list(self, val):
        self._list = val
        self._listsquare = [x**2 for x in self._list ]

    @property
    def listsquare(self):
        return self._listsquare
    @listsquare.setter
    def listsquare(self, val):
        self.list = [int(pow(x, 0.5)) for x in val]

>>> c = SomeClass(5)
>>> c.listsquare
[0, 1, 4, 9, 16]
>>> c.list
[0, 1, 2, 3, 4]
>>> c.list = range(0,6)
>>> c.list
[0, 1, 2, 3, 4, 5]
>>> c.listsquare
[0, 1, 4, 9, 16, 25]
>>> c.listsquare = [x**2 for x in range(0,10)]
>>> c.list
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Ignacio's @property solution is great but it recalculates the list every time you reference listsquare - that could get expensive. Mathew's solution is great, but now you have function calls. You can combine these with the 'property' function. Here I define a getter and a setter for my_list (I just couldn't call it 'list'!) that generates listsquare:

class SomeClass(object):

    def __init__(self, n=5):
        self.my_list = range(n)

    def get_my_list(self):
        return self._my_list

    def set_my_list(self, val):
        self._my_list = val
        # generate listsquare when my_list is updated
        self.my_listsquare = [x**2 for x in self._my_list]

    # now my_list can be used as a variable
    my_list = property(get_my_list, set_my_list, None, 'this list is squared')

x = SomeClass(3)
print x.my_list, x.my_listsquare
x.my_list = range(10)
print x.my_list, x.my_listsquare

This outputs:

[0, 1, 2] [0, 1, 4]
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9] [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

Absolutely. But use a property instead.

class SomeClass(object):
  def __init__(self, n=5):
    self.mylist = range(n)

  @property
  def listsquare(self):
    return [ x**2 for x in self.mylist ]

a = SomeClass()
a.mylist = [4, 5, 8]
print a.listsquare

Caching of the property value is left as an exercise for the reader.