From Chabad.org: And now the census results. After giving us the numbers for each tribe, the Torah gives us the grand total: 603,550. This number, however, does not include the Levites. Moshe was commanded by G‑d not to include the holy tribe in the general census. Instead, the Levites are assigned the following holy tasks: dismantling, carrying, and re-erecting the Tabernacle whenever the Jews traveled, and camping around the Sanctuary, keeping guard over it and its vessels.
The Torah spends so much time detailing the count of each tribe, and then adding it all up for the final count. And for what purpose? The point of the census was to prepare for battles, but if we are to have faith in G-d, why are numbers important? Many explain that counting something shows how precious you think it is, but if that’s why we counted, then why are the Levites left out? Are they less precious? If anything, they’re more precious because of the work they do. As Rashi explains, they Levites were counted separately, and not delineated here. Still, if every letter of every word in the Torah is to teach us something, there must be more to the detailed counting of the tribes.