Help me add outputs from a two 3 to 8 decoders
Easier to start with the binary and not decode it first. 

You will note that greater then 7 is a special case, as it implies that the carry out on a three bit adder will be 1 if and only if the sum of the two three bit inputs is larger then 7. 

The carry out from an adder stage is 1 if at least two of the three inputs (Cin, A,B) are 1, and we do not really care about the sum term, so we can write, Cout  = AB + C(A+B), which I make to be two 'or' and two 'and' gates per bit (Except the LSB where C is known to be 0 and this degenerates to a single and gate).

Where A,B are the two input bits and C is the carry in (0 for the first stage). 
Let F(A,B,C) be the logic element described above, then Out = F(a[2],b[2],F(a[1],b[1],F(a[0],b[0],0))). Out will be one only if the sum exceeds 7. 

5 And terms, 4 Or terms, purely combinatorial logic, but note that the output will be prone to glitches on input transitions as there are race paths.