jmc

We have $8$ choices for president, $7$ choices for vice-president, and $6$ choices for treasurer, for a total of $8\times 7\times 6=336$ choices. Now we have to subtract the number of choices that don't satisfy the requirement, where the $3$ officers are all boys or all girls. For either case, we have $4$ choices for president, $3$ choices of vice-president, and $2$ choices for treasurer, a total of $4\times 3\times 2=24$ choices. So we have $2\times 24=48$ total choices that don't satisfy the requirement.

Thus, there are $336-48=\boxed{288}$ good choices.