What it has probably done is create a 160 GB partition on your new drive to exactly reflect the original one, and you will have another partition, or unpartitioned space, of about 350 GB.
As you don't say what operating system you are running, RIGHT click on the 'Start' button, then click on 'Explore' and see if you have an extra drive letter listed. if you do, this is probably where your missing gigabytes are. If you don't have an extra drive letter, then your missing space probably is not set as an active partition.
Click on 'Start', then RIGHT click on computer then click on 'Manage'. From the screen that then appears choose 'Stroage / Disk management' and you will see a picture of your drives which will show any space that is not actively partitioned. You can use this screen to set space to an active partition. Just be aware that the total space shown on this disk will be about 465 GB, not 500. This is because the gigabytes being measured are not quite the same! It's the difference between salesman's language and engineer's language.
You say you have formatted these 160 GB since you cloned it. In that case it might be worth your while to just set the whole disc to one maximum sized partition before you try cloning again. It may still give you one partition of 160GB, but that's where the rest will be.