First you need to make sure the Jetpack plugin is activated and the shortcode module is turned on.

A video in your google drive can be embedded:

1. Upload to GoogleDrive
2. Open The Google Video page and choose Share from the vertical ellipsis at the top right.
3. In the Advanced settings make the video Public on the Web
4. From the vertical ellipsis menu choose open in a new window.
5. In the window that opens choose embed from the  vertical ellipsis menu.
6. copy the embed code and paste into the editor in the Text view.
7. on saving it will be converted into a shortcode like this:

[googleapps domain="drive" dir="file/d/1H-oJO4UbdAuxXRYCFEJJo-ZwYKA4CR0C/preview" query="" width="640" height="480" /]