Can hydrocodone or oxycodone cause insomnia?

Oxycodone:

Side effects include:

Constipation, nausea, sedation/somnolence, dizziness, lightheadedness, vomiting, pruritus, headache, insomnia, dry mouth, sweating, asthenia.

Hydrocodone:

Side effects include:

Lightheadedness, dizziness, sedation, nausea, vomiting, constipation. Adverse effects occur infrequently with usual oral antitussive dosages.

With extended-release capsules for chronic pain: Constipation, nausea, somnolence, fatigue, headache, dizziness, dry mouth, vomiting, pruritus, abdominal pain, peripheral edema, upper respiratory tract infection, muscle spasms, urinary tract infection, back pain, tremor.

With extended-release tablets for chronic pain: Nausea, constipation, vomiting, dizziness, headache, somnolence, fatigue, pruritus, tinnitus, insomnia, decreased appetite, influenza.

Source: Drugs.com

Not that I have ever heard of. They are actually supposed to make you tired. They always do for me when I first start taking them, but it wears out. But, I take some of that back, back in the early 2000's when I was on OxyContin, thay definately kept me awake! I don't think they make those anymore.
And Oxycodone is stronger than Hydrocodone.