Magic square with equal products

Question

Can we form a $2n \times 2n$ magic square, where $n \in \mathbb{N}$, such that the product of the numbers of the columns, rows, diagonals should be equal and no number should be repeated?

I have proved that for $2 \times 2$ it is not possible.

Answer 1

$$ \begin{array}{|c|c|c|c|} \hline 1 & 15 & 24 & 14\\ \hline 12 & 28 & 3 & 5\\ \hline 21 & 6 & 10 & 4\\ \hline 20 & 2 & 7 & 18\\ \hline \end{array} $$ Numbers used: $1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 18, 20, 21, 24, 28$
Magic product: $5040$
[Hey, that's $7!$]

Source: Multiplication Magic Square - Wolfram MathWorld

Answer 2

Lots of such squares are possible, including pandiagonal ones. Following is a 6×6 example which I developed and had published on www.multimagie.com. This is probably the 6×6 pandiagonal square with the lowest possible product ($46656000000$) and lowest corresponding maximum entry $1800$. The blue block is an example of a 3×3 block, all of which have the identical product $216000$.