27x³ - 27x² y + 9xy²-y³ - 20x³ + 15x² y - 4xy² + 3y³ + 10x³ + 12x² y - 5xy² + y³

To simplify the given expression:

Step 1: Combine like terms 27x³ - 27x² y - 20x³ + 10x³ = (27x³ - 20x³ + 10x³) - 27x² y = 17x³ - 27x² y

9xy² - 4xy² - 5xy² = (9xy² - 4xy² - 5xy²) = 0xy² = 0

-y³ + 3y³ + y³ = (-y³ + 3y³ + y³) = 3y³

15x² y + 12x² y = (15x² y + 12x² y) = 27x² y

Step 2: Combine terms using the simplified expressions from above 17x³ - 27x² y + 0 + 3y³ + 27x² y = 17x³ + 3y³

Therefore, the simplified expression is 17x³ + 3y³.