120 mm fork with a frame designed for 100 mm fork?
Before starting, your fork looks pretty nice. Are you sure you can't send it to FOX and rebuild it? Why do you say it is ruined?
About the fork size, please check the cube FAQ:

CAN I INSTALL FORKS WITH MORE TRAVEL AS PROVIDED IN THE STANDARD EQUIPMENT?
NO. The installation of a fork with more travel will void the warranty. The bike geometry will be changed in a negative way, which leads to a different handling of the bike and can damage the frame permanently.
It is also not approved to install double bridge forks into CUBE bikes.

If your bike is still under warranty, I don't think it is worth it. If it isn't, it will for sure put more stress on the frame but I don't think it will brake. This depends a lot of your weight and ride style, and keep in mind Cube says not to do it, so it is your entire responsibility. I wouldn't do it.
I am pretty sure you can change your suspension between 80, 100 and 120mm of travel. Please check here. Rock Shox has really good manuals so you might even be able to do it yourself, otherwise take it to your bike shop.
Changing a suspension is simple, if you have the patience and the time to learn, and you just need one or two allen tools for most of it. However, sometimes taking the bottom part of the headset from the old fork is a pain. Search on youtube for fork replacement. If you feel like it, I think you can try and if something goes wrong take it to a shop in pieces. They will figure it out :)
Before buying, confirm with the seller the fork will fit the frame, specially if it is an used fork he might have shorten the part of it that goes into the headset and it's shorter size might not fit your frame or your favorite stem position.
IMPORTANT: Please see @mikes comment below.