Although bucky ball is an allotropic form of carbon but it is included in organic chemistry?

Ans; Buckyballs are extremely stable in the chemical sense. Since all the carbon-carbon bonds are optimized in their configuration, they become very inert, and are not as prone to reactions as other carbon molecules. 

What makes these bonds special is a property called aromaticity. Or buckyballs have some degree of aromaticity. 

Normally, electrons are fixed in whatever bond they constitute. Whereas in aromatic molecules, of which hexagonal carbon rings are a prime example, electrons are free to move (“delocalize”) among other bonds. Since all the fullerenes have the cyclo-hexanes in abundance, they are very aromatic, and thus have very stable, inert, carbon bonds. Buckyballs, though sparingly soluble in many solvents, are in fact the only known carbon allotropes to be soluble.