Declare and initialise 3-dimensional array

Not at this time, although something like the following isn't too bad

A = zeros(2,2,2)
A[:,:,1] = [1 2; 3 4]
A[:,:,2] = [10 20; 30 40]

One can use either the cat or the reshape functions to accomplish the task: (tested with Julia-1.0.0):

julia> cat([1 2; 3 4], [5 6; 7 8], dims=3)
2×2×2 Array{Int64,3}:
[:, :, 1] =
 1  2
 3  4

[:, :, 2] =
 5  6
 7  8

For higher Array dimensions, the cat calls must be nested: cat(cat(..., dims=3), cat(..., dims=3), dims=4).

The reshape function allows building higher dimension Arrays "at once", i.e., without nested calls:

julia> reshape([(1:16)...], 2, 2, 2, 2)
2×2×2×2 Array{Int64,4}:
[:, :, 1, 1] =
 1  3
 2  4

[:, :, 2, 1] =
 5  7
 6  8

[:, :, 1, 2] =
  9  11
 10  12

[:, :, 2, 2] =
 13  15
 14  16