Thanks for the video. That is extremely helpful to us. Let’s start with the two Cores that are flashing green. As the troubleshooting guide mentions, the most common reason for their being unable to connect to Wi-Fi is that they are underpowered. I’m not sure how they are being powered, but the CC3000 requires up to 300mA of current during startup, so we recommend using a wall wart adapter that’s commonly used for smartphone chargers (rated for 500mA to 1A). If you’re using an unpowered USB hub (or even a powered one, especially with 3 Cores connected), it may be that they’re not receiving enough power to connect. Try powering and configuring just one at a time.
If your Cores are still not connecting, try the other common fixes–clearing the CC3000 SSID/password memory or a factory reset. And, of course, double check your network password 
Those are all documented at the link in my last post.
For the Core that only flashes white, this seems like a less common problem that could be caused by a variety of issues. Does it continue to flash white if you perform a factory reset? Is the Core heating up more than your other Cores?
Another one of our customers who had this issue was able to resolve it by testing on another network. Could you verify that you have the same issue after a factory reset and testing on a new network? That will help us narrow down the list of potential causes.