Another Inequality!

Algebra Level 5

\[\large{(a^3 +3)(b^3 + 6)(c^3+12) > k(a+b+c)^3}\]

Find the largest integer \(k\) such that for all positive integers \(a,b,c\), the above inequality satisfies.

Bonus - Can you find the largest real number \(k\) satisfying the above inequality?

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