Find the polynomial \(p(x),\) with real coefficients, such that \(p(x^3) - p(x^3 - 2) = [p(x)]^2 + 12 \) for all real numbers \(x.\)

Find the polynomial \(p(x)\), with real coefficients, such that \(p(x^3) - p(x^3 - 2) = [p(x)]^2 + 12\) for all real numbers \(x\).

\(p(x) = 6x^3-6\)

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