Sum of a square and a cube

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.

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