The Wolfram Programming Cloud makes it easy to embed videos into your cloud documents.
The following Cloud CDF shows how to create a package which implements a YouTube function which takes a videoid and optional settings to create this embedding. The key function to perform the embedding is EmbeddedHTML:
https://www.wolframcloud.com/objects/bb871f6e-169a-46d3-aa26-eb2026f0531d
The link above includes many example of use, but here is one typical example:
