  The octupole strengths of $\beta$-stable nucleus $^{208}_{82}Pb_{126}$, a
neutron skin nucleus $^{60}_{20}Ca_{40}$ and a neutron drip line nucleus
$^{28}_{8}O_{20}$ are studied by using the self-consistent Hartree-Fock
calculation plus the random phase approximation (RPA) with Skyrme interaction.
The collective properties of low-lying excitations are analyzed by using
particle-vibration coupling. The results show that the lowest isoscalar states
above threshold in $^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$ are the
superpositions of collective excitations and unperturbed transitions from bound
state to nonresonance states. For these three nuclei, both the low-lying
isoscalar states and giant isoscalar resonance carry isovector strength. The
ratio B(IV)/B(IS) is checked. It is found that, for $^{208}_{82}Pb_{126}$, the
ratios are equal to $(\frac{N-Z}{A})^2$ in good accuracy, while for
$^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$, the ratios are much larger than
$(\frac{N-Z}{A})^2$. This results from the excess neutrons with small binding
energies in $^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$.
