My sons, at the time ages 6 and 8, received a small inheritance from their grandfather. It was spelled out in a trust for them and was disbursed to them roughly 2 years after his death. Are they subject to taxes on this amount? Do I have to file anything for them with either the state or the federal government? Or are they exempt because of their age, and the fact that it was executed as a trust?

No you do not need to report this. There is no federal inheirtance tax.
I am ex-IRS

Agreed; the amont in question is so small as to NOT be subject to federal estate or state inheritance taxes.

Thanks for the help. I gather from the response, however, that the amount might determine whether anything needs to be filed? Is this correct?

Yes, the amount matters, but only if the amount exceeds about $1 MILLION.

If the amount being transferred was in that range, you would NOT be asking for advice on this forum; you would be seeking advice from an estate planner, an estate attorney, a CPA, or all three!

Thanks! And, no, it is oh so much smaller than a million dollars - so I guess I don't have to do anything except get a start on their college saving fund! Thanks for all your help!

Glad to help!