python nested classes

My version of your code, with comments:

#
# 1. CamelCasing for classes
#
class Account:
    def __init__(self):
        # 2. to refer to the inner class, you must use self.Bank
        # 3. no need to use an inner class here
        self.bank = self.Bank()

    class Bank:
        def __init__(self):
            self.balance = 100000

        # 4. in your original code, you had a method with the same name as 
        #    the attribute you set in the constructor. That meant that the 
        #    method was replaced with a value every time the constructor was 
        #    called. No need for a method to do a simple attribute lookup. This
        #    is Python, not Java.

        def withdraw(self, amount):
            self.balance -= amount

        def deposit(self, amount):
            self.balance += amount

a = Account()
print(a.bank.balance)

There are several problems:

1. You're using the name balance for both the data member and for the function.
2. You're missing a return statement in balance().
3. balance() operates on an instance of bank. There is no instance in a.bank.balance: here, a.bank refers to the inner class itself.

a.bank is the class (not instance) since you've never created an instance of the bank on a. So if a.bank is a class, a.bank.balance is a method bound to that class.

This works however:

class account:
    def __init__(self):
        self.bank = account.bank()

    class bank:
        def __init__(self):
            self.balance = 100000

        def whitdraw(self, amount):
            self.balance -= amount

        def deposit(self, amount):
            self.balance += amount

a = account()
print a.bank.balance

Of course, as you show working code without nested classes, It really begs the question about why you want to use nested classes for this. I would argue that the non-nested version is much cleaner.