Yes...two established tanks running
Hello; Stick the sponge filter in an established tank for a few weeks. It will become seeded with the beneficial bacteria (bb). I am guessing this is what you mean by "cycling a sponge filter".
If you plan to use the sponge filter in an established tank there is no more to do than stick it in.
If you plan to use it in a new setup, then the new tank setup will have to be "cycled" the same as any new setup. You have the advantage of having established tanks on hand. You can seed bb into the new tank with most any solid material from the established tanks. The bb will be on solid surfaces, substrate, plants, filter media, decorations and such.
I have often set up bare tanks quickly with only a bubbler operated sponge filter. I like to keep some free floating live plants like hornwort around to throw in such a tank. A bit of substrate in a mesh bag also works. It can still take a bit of time to get a good culture of bb going and in balance with the fish load, but having a starter culture of bb from the established tanks speeds things up a bit.
good luck