The palindromic number $595$ is interesting because it can be written as the sum of consecutive squares: $6^2+7^2+8^2+9^2+{10}^2+{11}^2+{12}^2$.

There are exactly eleven palindromes below one-thousand that can be written as consecutive square sums, and the sum of these palindromes is $4164$. Note that $1=0^2+1^2$ has not been included as this problem is concerned with the squares of positive integers.

Find the sum of all the numbers less than ${10}^8$ that are both palindromic and can be written as the sum of consecutive squares.