Do you work in the IT department of a School or University?
Say each CPU gave 15 sol/s mining zcash then your total would only be 480 sol/s and each instance would be mining low difficulty.
From my 2x7990 I am getting 630 sol/s which uses much less power and costs far less to purchase than 32 x CPU.
It would only be profitable because you said electric was free and you already owned your rig.
However you didn't state which algorithm/crypto and I guess everything would rely heavily on that so who knows really.
I have read that CPU mining burns them out pretty quickly so the longevity of such a miner is also a consideration.
But if you don't care about power costs and don't really care about the hardware this would be very profitable as of the total volume/hashrate you have.
There are people who use botnets to mine so it must be somewhat profitable