The problem is as follows:
Find the sum of the digits of $B$:
$B=\sqrt[3]{1224 \times 1225\times 1226+35\sqrt[3]{34\times35\times36+35}}$
The possible answers given in my book are as follows:
$\begin{array}{ll} 1.&10\\ 2.&18\\ 3.&9\\ 4.&12\\ \end{array}$
I've been tempted to use a calculator but this problem is meant to be solved by hand.
Does there exist a trick or anything for doing this, other than going by the brute force method of doing all the operations one by one?. How can this be simplified or solved quickly?. Can someone help me here?.