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Multiples of 4 can be written as 4k, for some integer k.
The first three digits multiple of 4 is 4*25=100, and the last is 4*249=996.
So, the sum of all the three digits multiples of 4 is
We know how to sum the first integers, but we need to sum the first 249 integers starting from 25, so we can rewrite our sum using this little trick:
In other words, we're summing all the first 249 integers, but then we remove the first 24. As a result, we have the sum of all integers from 25 to 249:
So, we have
And in both cases we can use the formula
And we have
Which evaluates to