If sequence $\{a_n\}$ has no zero term and satisfies that, for any $n\in\mathbb{N}$, $$(a_1+a_2+\cdots+a_n)^2=a_1^3+a_2^3+\cdots+a_n^3$$ - Find all qualifying sequences $\{a_1, a_2, a_3\}$ when $n=3$. - Is there an infinite sequence $\{a_n\}$ such that $a_{2013}=-2012$? If yes, give its general formula of $a_n$. If not, explain.