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?

You could use this
$$\eqalign{
    & {(\sin a + cosa)^3} = \sin {a^3} + cos{a^3} + 3\sin a \cdot cosa\left( {\sin a + cosa} \right)  \cr 
  &  \Rightarrow {\sin ^3}a + co{s^3}a = {(\sin a + cosa)^3} - 3\sin a \cdot cosa\left( {\sin a + cosa} \right)  \cr 
  & and  \cr 
  & {(\sin a + cosa)^2} = 1 + 2\sin a \cdot cosa  \cr 
  &  \Rightarrow \sin a \cdot cosa = {{{{(\sin a + cosa)}^2} - 1} \over 2}  \cr 
  & then : \sin a + cosa = k  \cr 
  &  \Rightarrow {\sin ^3}a + co{s^3}a = {k^3} - {3 \over 2}k({k^2} - 1) =  - {k \over 2}({k^2} - 3) \cr} $$
