If $y=2 x+1$, then what is the value of $\left(8 x^3-y^3+6 x y\right) ?$

-1 

Given,

y = 2x + 1

We know that,

 (a – b)³ = a³ – 3a²b + 3ab² – b³

= 2x - y = (-1)

= (2x - y)³ =  (-1)³

= 8x³ - 12x²y + 6xy² - y³ = -1

=  8x³  - 6xy(2x - y) - y³  = -1

= 8x³ - 6xy × (-1)  - y³  = -1

= 8x³  + 6xy - y³  = -1

=  8x³  - y³  + 6xy = -1

Method 2

Put the values of x = 1 and then we get y = 3

Put them in required equation.