The following program is one way of computing the sum of digits in a number.  It works properly for the first case, but fails for the second one.

def digitsum(num):
    digsum = 0
    tnum = num
    while tnum > 0:
        print("tnum = %d, digsum = %d" % (tnum,digsum))        
        digsum += (tnum % 10)
        tnum = int((tnum - (tnum % 10)) / 10)
    return digsum

print(digitsum(9999999999999999))
print(digitsum(99999999999999999))