Algebra

Ok, we have to do a number of things to set up this equation. 

First off, we know that $(a+b)^2=a^2+2ab+b^2$

Plugging in the values we know, we get that 

$4^2=6+2ab\\ 10=2ab\\ ab=5$

It is crucial for us to know this information. 

Now, let's take a look at a^3+b^3. 

We know that $(a+b)^3=a^{3}+3a^{2}b+3ab^{2}+b^{3}$

Now, take a look at the middle two terms. We can factor them to get $(a+b)^3=a^{3}+3ab(a+b)+b^{3}$

We already know all these terms! We get

$4^3=3(5)(4) +a^3+b^3\\ 64-60=a^3+b^3\\ 4=a^3+b^3$

So 4 is our answer!

Thanks! :)