Does the iPod Touch 6th Generation 16GB storage fill up fast?

Could be due to corrupted files

OTHER

Connect the iPod to your computer and look at the storage used by the various categories as shown in the colored bargarph in iTunes.

Come back with the results.

An "other" larger than about 1 1/2 GB indicates corrupted files.

What is the Other on my iPhone and How to Remove It

What is "Other" and What Can I Do About It?

Next, usually restoring from backup eliminated the corrupted files. However, sometimes restoring to factory settings/new iPod is required.

To restore from backup see:

iOS: How to back up

To restore to factory settings/new iPod see:

Use iTunes to restore your iPhone, iPad, or iPod to factory settings

I have a 32gb iPod touch 6. It is using 24 gbs and has 2 usable ones left. This is about 600 photos, 2 tv shows, 75 apps, and somewhere around 150-200 songs. All the other used space is from software upgrades and I am on the latest. I upgraded from a 16 gb iPod touch 4 which I had for two years and never really had a space problem. Unfortunately, current IOS apps tend to take up more space than when I was on with IOS 6 and software updates take up a lot of space. An out of the box iPod touch 6 comes with IOS 8.4(or at least when I got mine in July) and IOS 8 I believe was an update that took up 4 gb so this definitely uses a lot of space. Overall, it'll all depend on what you are using. I could download those photos to my computer to free space and I do have quite a few apps exceeding 1gb. You'd probably be able to have about half of what I currently have on my iPod if you got a 16gb.

It is going to depend on what you use it for. Apps, videos and pictures will fill up space quicker than music will.

If you put a lot of content on it in a short period, then yes.

If you put very little on it, then it may never fill up.

If you put a lot of content on it very slowly, then it will fill up slowly.