As I understand it, the OP was trying to do as it says in the book, to derive the formula shown next to Quadratic, but misunderstood what it said to do (which we can't see all of because the image is poorly composed) -- namely, to "multiply out" [MATH](\alpha +\beta)^3[/MATH] and rearrange (I think). Actually, I think the instructions we partially see are for deriving the Cubic formula, and the Quadratic formula must have been explained on the previous page.
Anyway, these formulas are not really "quadratic" and "cubic" but are to be
applied in solving certain very specialized problems involving the roots of quadratic and cubic equations (which I doubt are ever done in America).
And the OP then confused "equation for the sum of two cubes" with "formula for the cube of a sum" (namely the formula shown as "quadratic" in the book), which led everyone in the wrong direction.
We probably need to just let this go, unless the OP has specific questions. Lesson to
@Sonal7: show us more context, and ask questions very carefully, knowing that most of us probably are not familiar with the ways things are taught there.