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:

2285² + 20³
2223² + 66³
1810² + 125³
1197² + 156³

Find the sum of the five smallest such palindromic numbers.