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Sum of a square and a cube

Problem 348

Published on Saturday, 3rd September 2011, 04:00 pm; Solved by 1192

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.