How to discretize and solve a 3D Poisson Equation with Dirichlet boundary conditions owing to DifEqOperators

I love the following example of solving a 1D Poisson equation with DiffEqOperators.
However , I struggle to do the analog 3D example. Can somebody indicate me the right steps?

using DiffEqOperators, Plots
#Poisson Eq in 1D
#Δu = f with boundary conditions u(0) = 0 and u(1) = 0

Δx = 0.1
x = Δx:Δx:1-Δx # Solve only for the interior: the endpoints are known to be zero!
N = length(x)
f = sin.(2π*x)

Δ = CenteredDifference(2, 2, Δx, N)
bc = Dirichlet0BC(Float64)
u = (Δ*bc) \ f

u_analytic(x) = -sin(2π*x)/4(π^2)

plot(x, u)
plot!(x, u_analytic.(x))

In 3D, I could define Δ as:

Δxx = CenteredDifference{1}(2,2,Δx,N)
Δyy = CenteredDifference{2}(2,2,Δx,N)
Δzz = CenteredDifference{3}(2,2,Δx,N)
Δ = Δxx + Δyy + Δzz

But then, what to do ?
Thanks in advance for any kind of answer …