Find $\sin^3 a + \cos^3 a$, if $\sin a + \cos a$ is known 
Given that $\sin \phi +\cos \phi =1.2$, find $\sin^3\phi + \cos^3\phi$.

My work so far: 
(I am replacing $\phi$ with the variable a for this)
$\sin^3 a + 3\sin^2 a *\cos a + 3\sin a *\cos^2 a + \cos^3 a = 1.728$. (This comes from cubing the already given statement with 1.2 in it.)
$\sin^3 a + 3\sin a * \cos a (\sin a + \cos a) + \cos^3 a = 1.728$
$\sin^3 a + 3\sin a * \cos a (1.2) + \cos^3 a = 1.728$
$\sin^3 a + \cos^3 a = 1.728 - 3\sin a * \cos (a) *(1.2)$
Now I am stuck. What do I do next? Any hints?

Hint: To finish your last step you need to find an expression for $\sin a\cos a$ in terms of $\sin a+\cos a$. I'll help you here : 
$$
(\sin a+\cos a)^2=\color{green}{\sin^2 a}+2\color{#C00}{\sin a\cos a}+\color{green}{\cos^2 a}.
$$
You're searching for the red part, note that the green part is equal to ...
