Do the Warlock's Pact of the Tome cantrips need their material components?

Question

I want to create a celestial warlock and I want to have Shillelagh as one of my Pact of the Tome cantrips.

I also wanted wooden staff as an arcane focus so I can use melee and free up my other hand.

Are the Pact of the Tome cantrips treated as warlock cantrips, which would let me use my arcane focus, or would I need a separate Druidic focus?

For example, to cast Shillelagh you normally need to have mistletoe and a shamrock leaf. Would my warlock focus let me forego the need for the material components, or would I need a druidic focus too?

Answer 1

You may use your Arcane Focus

The Pact of the Tome description says...

When you gain this feature, choose three cantrips from any class’s spell list (the three needn’t be from the same list) [...] If they don’t appear on the warlock spell list, they are nonetheless warlock spells for you.

PHB108

and the Spellcasting section says...

Spellcasting Focus

You can use an arcane focus (see the Adventuring Gear section) as a spellcasting focus for your warlock spells.

PHB107

Thus, the extra cantrips gained by Pact of the Tome count as Warlock Spells for you, and you can use an Arcane Focus in lieu of zero-cost material components for your Warlock Spells.

Note

This addition to the Pact of the Tome description was added as Errata in the 5th Printing of the Player's Handbook. You may find the Errata pdf it is included in here

Answer 2

Most GMs don't worry about the minutia of what components are actually in a spellcasting pouch. Dungeons and Dragons is about adventures, not accounting, after all. If you know a spell, your character is presumably clever enough to gather components for whatever spells they may need. And as long as your component pouch is on hand, you can access what ever bits and bobs you need for casting.

That said, nothing about a Warlock's Pact Magic allows them to ignore material costs, but you wouldn't require a Druidic focus either. Your Grimoire of Shadows allows you to treat any cantrips granted by it as Warlock spells, regardless of what list they come from. Shillelagh would count as a Warlock cantrip for you, despite being a Druid cantrip.