Hello,
You can quickly verify if an IP is assigned to Googlebot below:
Verifying Googlebot
Incidentally, this isn’t Googlebot.
You say that when you publish, the IP is visiting just about all your posts. I assume that you mean that when you publish a new post that this IP visits most of your posts shortly afterwards. If this is the case then this does sound like it might be a content scraper bot looking for content to steal so that the owner of the bot can use your content to put on their own sites. Here are some handy tips if this is the case as this is a common problem:
Do you have RSS functionality on your site due to the speed with which they are scanning your site after you create new content? If so you may wish to switch to “Summary” for feeds on the WordPress “Reading” settings page.
You can try to find out if someone is actually stealing your content and placing it on their own sites by setting up “Google Alerts“.
Go to:
https://www.google.co.uk/alerts
They have a guide here:
https://support.google.com/websearch/answer/4815696?hl=en
In the Google alert page place some unique content from your new page wrapped in inverted commas in the search field. It will show a list of pages where Google sees this unique text. If there is nothing there that looks suspicious then you can click on the “Show options” link so that you can be sent an alert when Google does find another site with your unique content.
Once you have found the offending site or sites you can then carry out the following:
A) Send them a message to remove the offending content on their contact page or email if they have one. While many content thieves will ignore emails of this nature, others will take down your content as soon as you ask them to, especially if you mention that you will file a Digital Millennium Copyright Act (DMCA) infringement complaint against them if the article, post or page is not removed in a timely manner.
B) You also can file a Digital Millennium Copyright Act (DMCA) complaint against a site that has stolen your content. This can be done for Google, Bing & Yahoo below:
https://www.google.com/webmasters/tools/dmca-notice
https://www.microsoft.com/info/Search.aspx
https://policies.yahoo.com/us/en/yahoo/ip/index.htm
If they deem that another site actually has been stealing your content, then the site may be banned from search engines.
C) You can do a WHOIS search of the offending domain name and from the nameservers shown you can find out where they are hosting their site. You can file a DMCA complaint with the hosting provider. Some will investigate the issue and will in some cases suspend that hosting account unless they remove all stolen content and desist in stealing content in the future.
You can also block the IP address in Wordfence if they are stealing your content.