AMC 10 2021a Problem 11

For which of the following integers $b$ is the base-$b$ number $2021_b - 221_b$ not divisible by $3$? $\textbf{(A)} ~3 \textbf{(B)} ~4 \textbf{(C)} ~6 \textbf{(D)} ~7 \textbf{(E)} ~8$