Can you back up iCloud without WiFi

Technically, you could use Cellular Data or Ethernet, which I would only recommend if you have a good cellular plan and no wifi, or no internet and a WiFi router with an Ethernet jack, an ethernet cord, and an ethernet-supported device or an adapter for non-supported devices. Without Cellular or Ethernet, backing up a device and/or Apple Services requires an internet connection. However, backing up a device to iTunes on a PC or Mac does not require an internet connection, to my knowledge.

No you need Wifi for it to work.