I would want mouse and keyboard plugged directly into computer because of heavy use. The hub should use a rear rather than the weaker front sockets. That said not working at all indicates a problem or compatibility i.e USB hubs are mostly backward compatible but not all are.

 

I also bought a 3 port usb hub recently. It too has problems in that it allows 3 type A cables to be inserted, but only one port communicates with the motherboard. The other two have power but seem only seem to be present for charging or extra power to an appropriate usb cable.
There was nothing to indicate this on the packaging, and as such I put it down to
"You get what you pay for!"

Check to see that all ports communicate with the motherboard by swapping a thumb drive between each port, ejecting it safely before removing it.

 

Does the Hub has it's own power supply?
If devices are not being recognized, that means they are not receiving enough power from the USB port of the computer. Getting a hub with it's own power adapter should solve that.