Here's Exactly When To Order Your Cake From Costco's Bakery - Tasting Table
Briefly

Costco requires customers to place cake orders in person by filling out a paper form at a warehouse; there is no online form or phone number for cake orders. The form requires cake type, decoration description, contact information, and a pickup time. Orders must be placed at least 24 hours before pickup so bakers have enough time. Customers must make a separate trip to pick up ordered cakes, and pickups cannot occur on many store-closed holidays. For last-minute needs or holiday pickups, premade sheet cakes can be purchased and customized, with sizes and prices available for different serving counts.
Costco's cake ordering system is a bit of a rarity in today's technologically savvy world, as there's no online form you can fill out or even a number to call in order to place your order. Instead, you'll have to physically enter a Costco location and fill out a form specifying what kind of cake you want with a description of your desired decorations.
You need to place your cake order at least 24 hours before pickup; otherwise, it may not be ready in time. This means you can't simply head to Costco, order a cake, do some shopping, and pick it up at the end. You'll need to make two separate trips to the retailer: one to place the order, and one to pick it up. Also note that Costco is closed on many holidays, so don't plan on picking it up on those days.
If you forgot to place your order and need it within a few hours (or need to pick it up on a major holiday), your best bet is to purchase a premade cake and spiff it up yourself. If you have the time and resources to do this, it can be even better than a custom Costco cake, as you have complete control over the design and can even brag about being the designer to your friends and family.
Read at Tasting Table
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