Building blocks

Thinking of small building blocks, identical to one another, such as lego blocks, with an m x n grid of 'male' attaching points at the top and a 'female' attaching surface at the bottom, so if you have 1 x 1 blocks to combine, there is exactly one way to do it, as a tower, since they don't attach to the sides, just top to bottom. With two identical 2 x 2 blocks there are three ways, using all four connection pins, a row of two, or just one.

How many different ways are there to combine two 2 x 3 blocks?

How many different ways are there to combine three 2 x 2 blocks?