Distributional bilaplacian of the radial coordinate in three dimensions ($-{\Delta }^2|x|=8\pi {\delta }_0$)

In three dimensions, $\Delta |x|=2/|x|$ away from the origin and $-\Delta (1/|x|)=4\pi {\delta }_0$. Hence $-{\Delta }^2|x|=8\pi {\delta }_0$ as a distribution.