Find $ \left(a+b\right)^3 $ using formula

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

where $ A = a $ and $ B = b $.

$$ \left(a+b\right)^3 = a^3+3 \cdot a^2 \cdot b + 3 \cdot a \cdot b^2+b^3 = a^3+3a^2b+3ab^2+b^3 $$

Find $ \left(a-b\right)^3 $ using formula

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

where $ A = a $ and $ B = b $.

$$ \left(a-b\right)^3 = a^3-3 \cdot a^2 \cdot b + 3 \cdot a \cdot b^2-b^3 = a^3-3a^2b+3ab^2-b^3 $$

$$ \left( \color{blue}{a^3+3a^2b+3ab^2+b^3}\right) \cdot x = a^3x+3a^2bx+3ab^2x+b^3x $$

Multiply each term of $ \left( \color{blue}{a^3x+3a^2bx+3ab^2x+b^3x}\right) $ by each term in $ \left( a^3-3a^2b+3ab^2-b^3\right) $.

$$ \left( \color{blue}{a^3x+3a^2bx+3ab^2x+b^3x}\right) \cdot \left( a^3-3a^2b+3ab^2-b^3\right) = \\ = a^6x -\cancel{3a^5bx}+3a^4b^2x -\cancel{a^3b^3x}+ \cancel{3a^5bx}-9a^4b^2x+ \cancel{9a^3b^3x}-3a^2b^4x+3a^4b^2x -\cancel{9a^3b^3x}+9a^2b^4x -\cancel{3ab^5x}+ \cancel{a^3b^3x}-3a^2b^4x+ \cancel{3ab^5x}-b^6x $$

Combine like terms:

$$ a^6x \, \color{blue}{ -\cancel{3a^5bx}} \,+ \color{green}{3a^4b^2x} \, \color{orange}{ -\cancel{a^3b^3x}} \,+ \, \color{blue}{ \cancel{3a^5bx}} \, \color{red}{-9a^4b^2x} + \, \color{green}{ \cancel{9a^3b^3x}} \, \color{blue}{-3a^2b^4x} + \color{red}{3a^4b^2x} \, \color{red}{ -\cancel{9a^3b^3x}} \,+ \color{green}{9a^2b^4x} \, \color{orange}{ -\cancel{3ab^5x}} \,+ \, \color{red}{ \cancel{a^3b^3x}} \, \color{green}{-3a^2b^4x} + \, \color{orange}{ \cancel{3ab^5x}} \,-b^6x = a^6x \color{red}{-3a^4b^2x} + \color{green}{3a^2b^4x} -b^6x $$