Factorize: `a^3+3a^2b+3a b^2+b^3-8`

Explanation

To factorize the expression \( a^3 + 3a^2b + 3ab^2 + b^3 - 8 \), we can follow these steps:

### Step 1: Identify the structure of the expression
The expression \( a^3 + 3a^2b + 3ab^2 + b^3 \) resembles the expansion of the cube of a binomial, specifically \( (a + b)^3 \). The identity for the cube of a binomial is:
\[ (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 \]
Thus, we can rewrite the expression as:
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