Find $ \left(x+3h\right)^3 $ using formula

$$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$

where $ A = x $ and $ B = 3h $.

$$ \left(x+3h\right)^3 = x^3+3 \cdot x^2 \cdot 3h + 3 \cdot x \cdot \left( 3h \right)^2+\left( 3h \right)^3 = x^3+9hx^2+27h^2x+27h^3 $$

Find $ \left(x+2h\right)^3 $ using formula

$$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$

where $ A = x $ and $ B = 2h $.

$$ \left(x+2h\right)^3 = x^3+3 \cdot x^2 \cdot 2h + 3 \cdot x \cdot \left( 2h \right)^2+\left( 2h \right)^3 = x^3+6hx^2+12h^2x+8h^3 $$

Find $ \left(x+h\right)^3 $ using formula

$$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$

where $ A = x $ and $ B = h $.

$$ \left(x+h\right)^3 = x^3+3 \cdot x^2 \cdot h + 3 \cdot x \cdot h^2+h^3 = x^3+3hx^2+3h^2x+h^3 $$

Multiply $ \color{blue}{3} $ by $ \left( x^3+6hx^2+12h^2x+8h^3\right) $ $$ \color{blue}{3} \cdot \left( x^3+6hx^2+12h^2x+8h^3\right) = 3x^3+18hx^2+36h^2x+24h^3 $$Multiply $ \color{blue}{3} $ by $ \left( x^3+3hx^2+3h^2x+h^3\right) $ $$ \color{blue}{3} \cdot \left( x^3+3hx^2+3h^2x+h^3\right) = 3x^3+9hx^2+9h^2x+3h^3 $$

Remove the parentheses by changing the sign of each term within them.

$$ - \left( 3x^3+18hx^2+36h^2x+24h^3 \right) = -3x^3-18hx^2-36h^2x-24h^3 $$

Combine like terms:

$$ \color{blue}{x^3} + \color{red}{9hx^2} + \color{green}{27h^2x} + \color{orange}{27h^3} \color{blue}{-3x^3} \color{red}{-18hx^2} \color{green}{-36h^2x} \color{orange}{-24h^3} = \\ = \color{orange}{3h^3} \color{green}{-9h^2x} \color{red}{-9hx^2} \color{blue}{-2x^3} $$

Combine like terms:

$$ \color{blue}{3h^3} \, \color{red}{ -\cancel{9h^2x}} \, \, \color{orange}{ -\cancel{9hx^2}} \, \color{red}{-2x^3} + \color{red}{3x^3} + \, \color{orange}{ \cancel{9hx^2}} \,+ \, \color{red}{ \cancel{9h^2x}} \,+ \color{blue}{3h^3} = \color{blue}{6h^3} + \color{red}{x^3} $$

Combine like terms:

$$ 6h^3+ \, \color{blue}{ \cancel{x^3}} \, \, \color{blue}{ -\cancel{x^3}} \, = 6h^3 $$