1. **State the problem:** Simplify the expression $$\sqrt[3]{54 a^3 b} + \sqrt[3]{7 a^3 b} - a \sqrt[3]{7 b}$$. 2. **Rewrite the cube roots to separate factors with perfect cubes:** $$\sqrt[3]{54 a^3 b} = \sqrt[3]{27 \cdot 2 \cdot a^3 \cdot b} = \sqrt[3]{27} \cdot \sqrt[3]{2} \cdot \sqrt[3]{a^3} \cdot \sqrt[3]{b}$$ $$= 3 \cdot a \cdot \sqrt[3]{2b}$$ Similarly, $$\sqrt[3]{7 a^3 b} = \sqrt[3]{a^3} \cdot \sqrt[3]{7 b} = a \cdot \sqrt[3]{7b}$$ 3. **Rewrite the expression with simplified parts:** $$3 a \sqrt[3]{2b} + a \sqrt[3]{7b} - a \sqrt[3]{7b}$$ 4. **Combine like terms:** Notice that $$a \sqrt[3]{7b} - a \sqrt[3]{7b} = 0$$, so they cancel out. 5. **Final simplified expression:** $$3 a \sqrt[3]{2b}$$ **Answer:** $$3 a \sqrt[3]{2b}$$