Factorize: `2sqrt(2)a^3+3sqrt(3)b^3+c^3-3sqrt(6)a b c`

Explanation

To factorize the expression \( 2\sqrt{2}a^3 + 3\sqrt{3}b^3 + c^3 - 3\sqrt{6}abc \), we can follow these steps:

### Step 1: Identify the structure of the expression
We notice that the expression resembles the form of the identity for the sum of cubes:
\[ a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - ac - bc) \]
We can rewrite the given expression in a similar form.
...