$Obvious$ is a $Dangerous$ $word$ in Mathematics

First of all, the number should be a cube .

Secondly, it should be a two digit number.

We get : $27$ and $64$

$27$ satisfies the conditions.

And $27$ has $1,3,9,27$ as factors .

The number is 27!!!

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from math import *
def factors(n):    
    return set(reduce(list.__add__, 
                ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
def sum(n):
    summ=0
    for i in str(n):
        summ+=int(i)
    return summ
for i in range(10,100):
    if i**(1/float(3))==float(sqrt(sum(i))):
        print len(factors(i))

I used same approach, but checked it with code :)

There are only two two-digit cubes and this are $27$ and $64$ .

OBVIOUS that only $27$ satisfies the condition.

Since $27$ has $4$ divisors $=> 4$ is answer