CN-LEAGUE 2012 Problem 10

Given a sequence $\{a_n\}$ whose terms are non-zero real numbers. For any positive integer $n$ , the equality $$(\sum_{i=1}^{n}a_i)^2=\sum_{i=1}^{n}a_i^3$$ holds.(1) If $n=3$ , find all possible sequence $a_1,a_2,a_3$ ;(2) Does there exist such a sequence $\{a_n\}$ such that $a_{2011}=-2012$ ?