if Sm denotes sum of squares of first m natural numbers then for how many m<100 is Sm multiple of 4?
24
$\left(
\begin{array}{cc}
7 & 140 \\
8 & 204 \\
15 & 1240 \\
16 & 1496 \\
23 & 4324 \\
24 & 4900 \\
31 & 10416 \\
32 & 11440 \\
39 & 20540 \\
40 & 22140 \\
47 & 35720 \\
48 & 38024 \\
55 & 56980 \\
56 & 60116 \\
63 & 85344 \\
64 & 89440 \\
71 & 121836 \\
72 & 127020 \\
79 & 167480 \\
80 & 173880 \\
87 & 223300 \\
88 & 231044 \\
95 & 290320 \\
96 & 299536 \\
\end{array}
\right)$
there may be some clever way of doing this that one of our number theory experts can comment on.