The first bomb is somewhat understandable, still you could argue that the US might have figured out a way to demonstrate its destructive power to the Japanese without killing over 100,000 mostly innocent people in an instant. Maybe at the trade-off of temporarily risking US soldier lifes and resources of the general public. Still, you can argue the other way and see it as a terrible conclusion to a terrible war.
But the second one? I've seen many docs and historians perspectives on why it was considered necessary, but I can't find the point of view from which it was anything but a total atrocity for which the people who made it happen should be remembered in shame forever. So much of Japan not immediately surrendering after the first bomb dropped was down to the fog of war, to simple and understandable slow speed in government decisionmaking, etc.
Even if you can't be sure that the first bomb would have been enough to have them surrender, just the chance of it should have been enough to pick a different strategy, at the chance of saving a couple of dozen thousand innocent lives.