Magic Product Squares

In the second part of an earlier puzzle,
I asked for the smallest product for a 3x3
Magic Product Square.
For this puzzle, I'd like to know what the second and third smallest
products are, and give an example of each.

What are the smallest and next smallest products in a 4x4
magic product square? Consider just rows, columns and two main diagonals.
(For more fun, add in (1) the four corners, (2) each quadrant, and (3) the
four center squares.)
Give examples.

What are the smallest and next smallest products in a 5x5
magic product square? Consider just rows, columns and two main diagonals.
Give examples.
Source: Original.
Based on an earlier puzzle and a suggestion from Denis Borris.
Solution
Mail to Ken