Create a new document in Publisher in the page format you use most often. Insert a text box. By default, the style used in it will be Normal style. Then choose Home>Styles and right-click on Normal under the Styles in Use subhead. Choose Modify. Click on the Font button and change the Latin font to Cambria. OK out.
Delete the text box, then choose File>Save As. Change the Save as type dropdown to Publisher Template (*.pub) and save the file.
Then, when creating a new document, choose File>New>Custom Office Templates and select the template you had created. Create a text box and check that the font is now set to Cambria instead of Calibri.