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?

Squaring
$\sin a + \cos a = b$,
$b^2
=\sin^2a+2\sin a \cos a + \cos^2 a
= 1+2\sin a \cos a
$,
so
$\sin a \cos a
=(b^2-1)/2
$.
