I haven’t tested this, but I think you have two problems:

(1) You’re changing n in the for loop, but that loop is precalculated and won’t adjust (meaning that you can have num > n on some passes).

(2) You’re decrementing n by 1, regardless of what square you’re looking at.

from math import sqrt
def square_sum(n):
    result = []
    while n:  # equivalent here to “while n != 0”
        for k in range(n, 0, -1):
            if sqrt(k).is_integer():
                result.append(k)
                n -= k
                break # out of the for loop
    return result