Mould on Cactus Base, help

I have a large cactus with multiple heads which up until recently was thriving.

A few weeks ago I noticed white mould on the base of 2 of the heads and they had gone soft and wet. I thought I had overwatered it so I removed the damaged heads and repotted the rest in new dry soil. I've been careful not to overwater since. However I've now got mould on 2 further heads, one of which has gone soft.
I'm wondering if it's mealy bugs or a fungus but it's not clear from Internet searches.

I've had this cactus for a long time and it was grown from one given to my aunt by my great grandmother so I don't want to lose it. Any help or advice would be appreciated. Thanks.

 

Could be wrong but it could be mealy bugs, rather than rot.
Try painting it with methylated spirit, you might find tiny brown bugs in the wooly stuff.

 

Hi if it's mealy bug, you could wipe it with a cotton bud dipped in meths or isopropyl alcohol. That takes off the fluff and should kill them. If the fluff goes and you see an insect, you know that's it. If there isn't one, which means mould, you could use sulphur dusting powder on it to help reduce it.

 

Snap @pete!

 

Is the inside of the cactus rotten/brown, because if so it's dying. Once a cactus starts to rot inside there isn't much you can do about it. It has happened to several of mine over the years. The problem is often with the roots.
Mealy bugs seem to home in on a dying cactus.

For a few mealy bugs you can use methylated spirit, as described above, but a heavy infestation like that is more difficult to get rid of, and like I've said it usually means the cactus is dying.

 

I've found rot around the base is orange in colour and the cactus rots from the base up.
Obviously there are probably other types, and I agree, once rot gets into the flesh there is not much that you can do.