How to calculate the charge density in an electric field

I've been studying electric fields in class for some time and one thing is seemingly contradictory and really confuses me.

The charge density ρ is related to the electric field E and the permiativity ε and the potential [itex]\Phi[/itex] by the following equation

ρ/ε=∇[itex]\cdot[/itex]E=-∇²[itex]\Phi[/itex]

if we examine the electric field created by a single point charge of magnitude q located at the origin, then the electrostatic potential can be expressed as follows

[itex]\Phi[/itex]=[itex]\frac{q}{4πε(x^2+y^2+z^2)}[/itex]

now I would expect the charge density in this system to be zero everywhere except the origin but if we take the laplacean of this electric field, instead we get

ρ/ε=-∇²[itex]\Phi[/itex]=[itex]\frac{2q}{4πε(x^2+y^2+z^2)^2}[/itex]

which is clearly non-zero.

is there an explanation for this discrepancy? Have I violated some fundamental assumption?

thanks in advance