Continuous TypeError when attempting to add integers in a list?

I think the problem is simpler than you and other answers are making it. First rule of recursion is let the recursion do the work:

def addition_nest(unknown):
    if isinstance(unknown, list):
        if unknown:  # not empty
            head, *tail = unknown
            return addition_nest(head) + addition_nest(tail)

        return 0  # empty

    if isinstance(unknown, (int, float)):
        return unknown

    return 0  # neither list nor number

OTOH, if we want to reduce recursion and increase efficiency, we could move in the direction of something like:

def addition_nest(unknown):
    if isinstance(unknown, (int, float)):
        return unknown

    if isinstance(unknown, list):
        return sum(map(addition_nest, unknown))

    return 0

Which is still recursion, though indirectly as we don't directly call the function from itself but rather hand it off to map().

This code will get you the expected output.

def addition_nest(x):
    netsum = 0
    if isinstance(x, int):
    # if isinstance(x, (int, float)):
        return x
    elif isinstance(x, list):
        for each_element in x:
            if isinstance(each_element, int):
            # if isinstance(each_element, (int, float)):
                netsum += each_element
            elif isinstance(each_element, list):
                netsum += addition_nest(each_element)
        return netsum

print(addition_nest(25))  ## Output: 25
print(addition_nest([25, 30, 'a']))  ## Output: 55
print(addition_nest([25, 30, ['a', 10, 20]]))  ## Output: 85

If you want the above code to work with float also, replace the if conditions with the commented lines.

In your existing code, you have handled the scenarios for when an element inside the parent list is another list or an integer. But you didn't handle it for other data types. That is the reason for the error you are facing.

First of all, the third line is not used and pointless

sublist = []

Second, in cases that it is a list just simply call the function on every element and add together.

def addition_nest(x):
    netsum = 0
    sublist = []
    if isinstance(x, int):
        return x
    if isinstance(x, list):
        for sublist in x:
            netsum = netsum + addition_nest(sublist)
        return netsum

This will do.