some of the external links we have are on websites that have more than 300 to 500 outgoing links

I'm assuming that by this you probably mean external inbound links (aka "backlinks")... and that they are on pages that have 300 to 500 links (ie, from those pages). The title suggests the links are to such pages, which doesn't quite make sense to me. Please advise... and we can adjust the title if need be.

Assuming you mean that the links are from such pages... theoretically, if you didn't place these links, you needn't worry about them. I think you're correct that these pages are so "easy" that Google isn't likely to assume that you bought these, but I'm often amazed at what people do buy and how some "SEO" packages can surprise you.

Are you just doing a routine inspection of your backlinks, or are you reacting to a rankings drop or a message from Google? Do you have other reasons to worry?

And what are your other backlinks like? Has your content and promotion attracted some traffic and some natural links that clearly establish trust? If so, probably nothing to worry about.

I mean external back links that is correct that are on pages that have themselves 30 to 500 external back links. I was just doing a routing inspection of what back links I had. Just out of curiosity if one of the website I am on was hit by Panda or Penguin does it also hurt me ?

Mod's note: Changed thread title from...

Outbound links to external pages that have a large number of outbound links
to...
Backlinks from external pages that have a large number of outbound links

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Just out of curiosity if one of the website I am on was hit by Panda or Penguin does it also hurt me ?

I'm reading this as asking whether you would be affected if one of the sites or pages that had a backlink to you was hit by Penguin or Panda.

The more outbound links on a page, the less link juice any one of those links transmits. So the links on these pages would not have helped you very much to start with, and any loss of linking credit from them is similarly likely to be insignificant.

If all these pages were somehow related, though, say by common ownership or by being in the same network fed by common upstream linking sources, then you might be affected if a large group of them were hit.

Thank you that answers my questions