Q:

Is shear modulus only applicable to cubical solids?

Do we have any real life/theoretical examples where shear modulus is applicable to non-cubical shapes?

A:

The shear modulus is a property of the material not of the shape the material is cut into.
You normally see shear modulus explained using a cuboidal shape something like this:

But this is just because it's simpler to explain. If a non-cuboidal shape is deformed the shear stress won't be constant but will depend on the shape of the object and the way the deforming force is applied, and in general the shear stress field will be hard to calculate.
When doing numerical calculations we break down complicated shapes into tiny individual cells, and these can be (though don't need to be) cubic. So the overall behaviour is modelled as the behaviour of many tiny cubes. This is known as finite element analysis.

