  We compute the light asymptotic limit of $A_{n-1}$ Toda conformal blocks by
using the AGT correspondence. We show that for certain class of CFT blocks the
corresponding Nekrasov partition functions in this limit are simplified
drastically being represented as a sum of a restricted class of Young diagrams.
In the particular case of $A_{2}$ Toda we also compute the corresponding
conformal blocks using conventional CFT techniques finding a perfect agreement
with the results obtained from the Nekrasov partition functions.
