The time period of the revolution of an electron in an orbit is proportional to the cube of the principal quantum number, $n^3$. Therefore, the ratio of time periods for the second and third excited states is:
$$ \frac{T_2}{T_3} = \left(\frac{n_2}{n_3}\right)^3 = \left(\frac{3}{4}\right)^3 = 27 : 64 $$