A fabulous number

Let $n$ be an integer greater than $1$ . The positive divisors of $n$ are ${ d }_{ 1 },{ d }_{ 2 },\ldots,{ d }_{ k }$ , in which $1={ d }_{ 1 }<{ d }_{ 2 }<\ldots<{ d }_{ k }=n$ . If $n$ satisfies $n={ d }_{ 2 }^{ 2 }+{ d }_{ 3 }^{ 3 }$ , what is the sum of all the possible values of $n$ ?

This problem appeared at the Mexican MO.