2018 AMC 10B Problem 16

Let a_1,a_2,\ldots,a_{2018} be a strictly increasing sequence of positive integers such that a_1+a_2+\cdots+a_{2018}=2018^{2018}. What is the remainder when a_1^3+a_2^3+\cdots+a_{2018}^3 is divided by 6?

\textbf{(A) }0 \qquad \textbf{(B) }1 \qquad \textbf{(C) }2 \qquad \textbf{(D) }3 \qquad \textbf{(E) }4 \qquad

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.