Algebra

We can use the fact (a+b)3=a3+3a2b+3ab2+b3 to our advantage.

Expanding the left side, we get

$$\begin{align*} (a + b)^3 &= a^3 + 3a^2 b + 3ab^2 + b^3 \ &= a^3 + b^3 + 3ab (a + b). \end{align*}$$

Since we are given that a+b=4, this becomes a^3 + b^3 + 3ab(4) = 6.

Then a^3 + b^3 = −10​.