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?

Note
$$
x^3+y^3 = (x+y)\left(x^2-xy +y^2\right)
$$
Now we can see that if we set 
$$
x =\sin a\\
y = \cos a.
$$
Then we get
$$
\sin^3a+\cos^3a = (\sin a +\cos a)\left(1-\sin a\cos a\right)
$$
We can utilise
$$
(\sin a+ \cos a)^2 = 1 +2\sin a\cos a
$$
Combining all the above will yield 
$$
\sin^3a+\cos^3a = (\sin a +\cos a)\left(1-\frac{(\sin a+ \cos a)^2-1}{2}\right)
$$
