How to determine the edge length of the aluminium unit cell?
Correct approach is to do two things:

1)  Put four atomic masses into one unit cell.

2)  Properly extract the cube root of the volume you obtain.  That volume should now be about $6.6×10^{-23}\text{cm}^3$ from part 1.  To take the cube root properly, render the exponent on 10 as a multiple of 3, thus  $6.6×10^{-23}$ = $66×10^{-24}$ where $10^{-24}$, not $10^{-23}$, is $(10^{-8})^3$.

Then your numbers should work out.