With the HubSpot-Salesforce integration, you have the ability to add a HubSpot Intelligence window to your lead and contact page layouts. This window shows you information on that contact or lead's visit, page view, and submission information, as well as their HubSpot Score. This article will discuss why you might be seeing a blank HubSpot Score in this window if you expect to see one there:
The HubSpot Score in this window pulls from the HubSpot Score property in HubSpot, which is determined by whatever Manual Lead Scoring you have set up. At this time, this window is unable to show any score associated with Predictive Lead Scoring. So, if you've set up and are using Predictive Lead Scoring but not Manual Lead Scoring, this could be why your HubSpot Score is showing up as blank.