In this article, we theoretically analyze the Diels-Alder cycloaddition between cyclopentadiene and C-60 for which experimental results on energy barriers and reaction energies are known. The comparison of the results obtained with the two-layered ONIOM approach using different partitions for the high- and low-level layers with those obtained employing the B3LYP/6-31 G(d) method for the entire system allows us to conclude that the partition including a pyracylene unit of C-60 in the description of the high-level layer is enough to get excellent results. Using this partition in the two-layered ONIOM approach, we have computed the energy barriers and reaction energies for this Diels-Alder reaction for different functionals, and we have compared them with experimental data. From this comparison, both the ONIOM2(M06-2X/6-31G(d):SVWN/STO-3G) and the M06-2X/6-31G(d)//ONIOM2(B3LYP/6-31G(d):SVWN/STO-3G) methods are recommended as reliable and computationally affordable approaches to be exploited for the study of the chemical reactivity of [6,6]-bonds in fullerenes and nanotubes.