Sum of a square and a cube

If we list all the natural numbers below $10$ that are multiples of $3$ or $5$, we get $3, 5, 6$ and $9$. The sum of these multiples is $23$.

Find the sum of all the multiples of $3$ or $5$ below $1000$.

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.