External harddisk is not being recognized Mac10.10 & Win7: ICY BOX IB-231STU3-G & Samsung SSD 850Pro (2.5" 512GB SATA 6GB/s) on OSX 10.10.5

i suggest you take the drive back.

does either see the drive if it is plugged straight into the motherboard?

The box can be faulty.
If you have a PC the. Try to connect it directly to a SATA port and see if BIOS and Windows Disk Management are able to see it. If yes then your Icy Box is definitely bad.

you can also test if your system sees the disk witha normal laptop drive in it
that would exclude the icy box and cable

Is ICY box not recognized or hard drive inside not recognized?

Check the connection of the SATA from the SSD 850Pro to the ICY BOX IB-231STU3-G and also the USB cables connections.
If still not recognized you may have bad products, test individually if you can. and RMA the faulty product.

Your simple, change the light bulb test, would be to put another, known working, drive in the ICY BOX.  If it then appears, the Samsung SSD is bad.  If it doesn't, you either have a bad ICY BOX or a bizarre incompatibility issue with your USB ports.

Davis - you just reated my post

Out of the 4 possible options with faults in 2 devices, three  have been mentioned so far :)

Option 4: try the SSD in a known-to-work enclosure, a USB-2 type will suffice.

When I connect the box to a Windows machine it recognizes the USB Bridge(ICY Box) and the Samsung Magic tool sees the size of the ssd but it cannot run tests on it.

You NEED to try another hard disk drive in the Icy Box enclosure or connect the SSD directly to another PC without the enclosure.  Doing the second is pretty easy on a desktop.  Unplug and use the cables from the back of the CD/DVD drive.

@gheist - That 3.5W is for the 2TB drive, not the 512Gb drive

Specification is not very consistent about peak power draw for each model. Lets assume being close to worst.

Probably it's my usb port on my Macbook Air (2011). Currently I do not have another system where I do have admin rights. I have to check with a friend. It shows a red light when plugged to my Macbook Air and and Blue when it's plugged to machine with usb 3.0 ports(blue port).

Ok, but I don't see how you would need admin rights for testing a USB device. Does the enclosure need a driver installed?

USB 2.0 cannot feed your disk, especially not on laptops on battery with proper USB power limiter.
You might be able to help yourself with USB Y cable or powered USB hub.

Right but if I need to format the disk I need admin rights, right?

For a removable disk, you don't as far as I know. You can format a thumb drive, right?

ok  - so you need usb 3 - or a powered usb hub
and right click the drive - choose format
that should do it

I'd say drive has some undercurrent protection and plainly switches off in case it detects short power supply. You might be able to read number of such events via SMART (free tools are around nets to see SMART attributes)

I originally said:
"Check the connection of the SATA from the SSD 850Pro to the ICY BOX IB-231STU3-G and also the USB cables connections."
I forgot "&" between USB cables connections, but you understood!

I have a USB 3.0 1TB 2.5" external drive that is powered by a 10" netbook USB 2.5 and it supply's plenty of  Watts, so it is not a that a laptop supplies insufficient power, it is your Macbook Air (2011) that supplies insufficient power as you have stated:
"Probably it's my usb port on my Macbook Air (2011)."

If you have 2 spare USB ports, you can get a USB 3.0 2.5" external drive cable with two USB plugs (one for data + power the other for extra power)
If not then the twin USB cable with an USB charger would be allot cheaper and smaller than an USB 3.0 powered hub.

"When I connect the box to a Windows machine it recognizes the USB Bridge(ICY Box) and the Samsung Magic tool sees the size of the ssd but it cannot run tests on it."

Do you mean: Samsung Magician Software for PC?
Check you have the latest software for SSD.
Download Link:
http://www.samsung.com/global/business/semiconductor/minisite/SSD/global/html/support/downloads.html

@Michael-Best - 2 spare USB ports on a MacBook Air will not be practical, it has only 2 USB-2 ports, one on the left and one on the right side of the screen ;)

Some info from Apple on USB powered peripherals:
https://support.apple.com/en-us/HT204377

Confirming power usage in System Profiler
Open System Profiler to find more information about peripheral power requirements, or contact the manufacturer of your peripheral. For the most accurate information about power usage, make sure your device is connected directly to your Apple computer or display before opening System Profiler.

Thank you gheist. Your solution was correct. I was able to find a system with USB 3.0 where I had enough rights to format the disk. So basically I have a superfast disk :-) but now I need to find a way to power it sufficiently. :-(