## Sum of a square and a cube

### Problem 348

Many numbers can be expressed as the sum of a square and a cube. Some of them in more than one way.

Consider the palindromic numbers that can be expressed as the sum of a square and a cube, both greater than 1, in **exactly** 4 different ways.

For example, 5229225 is a palindromic number and it can be expressed in exactly 4 different ways:

2285^{2} + 20^{3}

2223^{2} + 66^{3}

1810^{2} + 125^{3}

1197^{2} + 156^{3}

Find the sum of the five smallest such palindromic numbers.