Use linearity and the formula ${\displaystyle \underset{j=1}{\overset{N}{}}}{j}^3=\frac{N^4}{4}+\frac{N^3}{2}+\frac{N^2}{4}to$ evaluate the $limit.$

$\underset{N}{lim}{\displaystyle \underset{i=1}{\overset{N}{}}}(\frac{i^3}{N^4}-\frac{21}{N})$

$(Express$ numbers $in$ exact form. Use symbolic notation and fractions where needed. Enter DNE $if$ the $limit$ does not exist.$)$