hi, I have been having some trouble doing this problem, could some one help me out?
If a+b=6, ab=4 find the value of a^3+b^3. (a+b)^3=a^3+3a^2b+3ab^2+b^3
I'm sorry if this is a bit unclear, the a^2 means a to the power of 2. thanks for the help.

Perhaps, try using the sum of two cubes factorization.

a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})

Then we get it down to (6)(a^{2}-4+b^{2})

Did they give you a^{2}+b^{2} by chance?

No they didn't, sorry, that was all that it said

Then we can finish by solving for a or b in the givens.

ab=4... [1]

a+b=6... [2]

From [1], a=4/b

Sub into [2]:

(4/b)+b=6

b=3-\sqrt{5}, \;\ \sqrt{5}+3

Now, can you finish up?

Yes, thank you for the help Galactus.

you may finish the solution #2 suggested by galacuts like this:
(a+b)^2=a^2 + b^2 + 2ab
36 = a^2+b^2 + 8 , therefore, a^2+b^2=28

now a^3+b^3 =(a+b)(a^2 + b^2 - ab)
=6 (28-4)=6(24)=144