1. **Problem:** Given $x + y = 12$ and $xy = 27$, find the value of $x^3 + y^3$.
2. **Formula:** Recall the identity for the sum of cubes:
$$x^3 + y^3 = (x + y)^3 - 3xy(x + y)$$
3. **Substitute known values:**
$$x + y = 12$$
$$xy = 27$$
4. **Calculate:**
$$x^3 + y^3 = 12^3 - 3 \times 27 \times 12$$
$$= 1728 - 972$$
$$= 756$$
**Final answer:** $x^3 + y^3 = 756$
Sum Cubes 389Ac8
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