In general, the dependency of a nominal strength of a material to the size of a specimen is called size effect. This phenomenon is very common in quasi-brittle and brittle solids and can be observed in either the compressive or the tensile strength of concrete. There are many papers in this field which could be found in this subject (Please see my papers entitled " Effect of size on nominal strength of self-compacting lightweight concrete and self-compacting normal weight concrete: A stress-based approach ", " Influences of water to cement ratio on brittleness and fracture parameters of self-compacting lightweight concrete ", " Effects of maximum aggregate size on fracture behaviors of self-compacting lightweight concrete ", and " Critical Crack-Tip Opening Displacement of SCLC " for further information.
In general, the dependency of a nominal strength of a material to the size of a specimen is called size effect. This phenomenon is very common in quasi-brittle and brittle solids and can be observed in either the compressive or the tensile strength of concrete. There are many papers in this field which could be found in this subject (Please see my papers entitled " Effect of size on nominal strength of self-compacting lightweight concrete and self-compacting normal weight concrete: A stress-based approach ", " Influences of water to cement ratio on brittleness and fracture parameters of self-compacting lightweight concrete ", " Effects of maximum aggregate size on fracture behaviors of self-compacting lightweight concrete ", and " Critical Crack-Tip Opening Displacement of SCLC " for further information.
As far as I know, the issue is related to the effect of the loading platens above and below the sample during the test, which restrict the failure of the sample and give it a higher resistance than its real value. This restriction is influenced by the ratio of height to width of the specimen. The longer the length of the sample (to some extent) the less the effect of the restriction, and since this ratio is equal to 2 for the cylinder (height / diameter) and 1 for the cube, the cube affects the restriction more than the cylinder and thus gives a higher value of compressive strength than the cylinder.
In addition to the "size effect" there is another theory of "weakest link" which also a deciding factor for strength if the size of the specimen increases.
Mohammed Salah Nasr I would like to add little more to Mohammed answer. As l/d is 2 for cylinder there is exactly a zone at the center which corresponds to pure compression and is the reason for initiation of vertical cracks which spread out or branch outwards because of the friction/restriction at both ends. Whereas no vertical cracking in cube.