Algebra

With the first equation, let's square both sides. We get

$a^2 + 2ab + b^2 = 16 \\ a^2 + b^2 = 16 - 2ab$

Now, we have a second equation of 

$a^2 + b^2 = 6 + 2ab$

Now, we simplfy subtract the first equation from the second one, we get 

$0 = -10 + 4ab \\ 10 = 4ab \\ ab = 10 / 4 = 5/2 \\ a^3 + b^3 = (a + b) ( a^2 + b^2 - ab) \\ a^3 + b^3 = (4) ( 6 + 2ab - ab) \\ a^3 + b^3 = (4) ( 6 - ab) \\ a^3 + b^3 = (4) ( 6 - 5/2) \\ a^3 + b^3 = (4) ( 7/2) \\ a^3 + b^3 = 14$

14 is our answer. 

Thanks! :)