`\frac{15^3 + 5 \cdot 15^2 - 5^3}{18^3 + 6 \cdot 18^2 - 6^3}`

`= \frac{(3 \cdot 5)^3 + 5 \cdot (3 \cdot 5)^2 - 5^3}{(3 \cdot 6)^3 + 6 \cdot (3 \cdot 6)^2 - 6^3}`

`= \frac{3^3 \cdot 5^3 + 5 \cdot 3^2 \cdot 5^2 - 5^3}{3^3 \cdot 6^3 + 6 \cdot 3^2 \cdot 6^2 - 6^3}`

`= \frac{27 \cdot 5^3 + 9 \cdot 5^3 - 1 \cdot 5^3}{27 \cdot 6^3 + 9 \cdot 6^3 - 1 \cdot 6^3}`

`= \frac{5^3 \cdot (27 + 9 - 1)}{6^3 \cdot (27 + 9 - 1)}`

`= \frac{5^3 \cdot 35}{6^3 \cdot 35}`

`= \frac{5^3}{6^3} `

`= \frac{125}{216}`

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