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.