Simplify: $\left(x + y\right)^{3}− \left(x − y\right)^{3} − 6y\left(x^{2} − y^{2}\right)$

$8y^{3}$

$\left(x + y\right)^{3}− \left(x − y\right)^{3} − 6y\left(x^{2} − y^{2}\right)$

We know that,

(x+y)³ = x³ + y³ + 3x²y + 3xy²

(x-y)³ = x³ - y³ - 3x²y + 3xy²

Applying the formula =

= x³ + y³ + 3x²y + 3xy² -(x³ - y³ - 3x²y + 3xy²) - 6y(x² - y²)

= x³ + y³ + 3x²y + 3xy² - x³ + y³+ 3x²y - 3xy² - 6yx² + 6y³

After eliminating the terms we get,

=  8y³