A Game of Numbers and Codes

Computer Science Level pending

Let \( K (n)\) equal the sum of the squares of all primes below \(n\), and let \(S (n)\) equal the sum of the cubes of all even numbers below \(n\).

If the value of \(n\) is the square-root of the sum of all non-negative perfect cube-root numbers below one-hundred, what is the value of \(3^x-2^x \), where \(x\) is the remainder when \(S (n)\) is divided by \(K (n)? \)

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