Use the standard identity for the sum of cubes: α^3+β^3 = (α+β)^3 - 3αβ(α+β). This identity is useful because the problem already gives the sum and product of the two roots. Here, Use α^3+β^3=(α+β)^3-3αβ(α+β). Thus 7^3-3(4)(7)=259. Be careful with negative signs when cubing the sum and multiplying the product term.