using DataFrames
A=reshape(1:24, 2,3,4)
idx=[Symbol("index$i") for i in 1:ndims(A)]
nts=[(;zip(idx,Tuple(t))...) for t in CartesianIndices(A)]
df=DataFrame(nts)
df.values=A[:]
df
or more succinctly
DataFrame([(;zip([idx;:values],(i.I...,a))...) for (i,a) in zip(CartesianIndices(A),A)])