In general, compressive strength of concrete cubes increases with the decrease in size of the cube. The same is also true for the cyliderical specimens having same height-to-diameter ratios.
In this connection, results of an interesting research study are available at the following link:
http://scialert.net/fulltext/?doi=jas.2011.584.588
Moreover, the size & shape of the concrete samples (cube or cylinder) to be used for determining the compressive strength of concrete is specified in the relevant Concrete Design code.
Although, generally 150x150x150 mm cubes are specified by the more common design codes, cube shaped or cylinderical specimens of other sizes may also be used for determining the design compressive strength of concrete, IF ACCEPTABLE BY THE APPLICABLE CONCRETE DESIGN CODE.
Regards.