Which numbers will replace the question marks ($?$) to logically complete the given series?
$$1,6,15,28,?,?,91$$

Let's find the difference between consecutive terms:
* $6-1=5$$\ast$ 15 - 6 = 9
* $28 - 15 = 13

The differences are $5,9,13,\dots$
Notice that the difference between these differences increases by $+4$ each time (a constant second difference):

* $9-5=4$
* $13-9=4$

Following this logic:

* Next difference should be $13+4=17$.
First missing term $=28+17=45$.
* Subsequent difference should be $17+4=21$.
Second missing term $=45+21=66$.

Let's check the next term to verify the pattern:

* Next difference should be $21+4=25$.
Term after $66=66+25=91$, which matches the given series.

Therefore, the missing numbers are $45$ and $66$.