Hello, thank you for the detailed and well-formulated question.
To answer your main question: The charge of $0.125 / 1M tokens applies each time you use the cached prompt in a request. It is not a one-time fee but the discounted input rate for the cachedContentTokenCount.
Cache price not as an extra fee, but as a big discount for reusing your prompt
Your second scenario, where the charge applies for every request, is the correct interpretation.
- Cached Input: The cachedContentTokenCount is billed at the discounted rate of $0.125 / 1M tokens.
- Standard Input: The new tokens (promptTokenCount - cachedContentTokenCount) are billed at the standard input rate of $1.25 / 1M tokens.
- Output: The total output cost is based on the sum of candidatesTokenCount and thoughtsTokenCount, billed at the standard output rate.
Therefore, your interpretation is correct. The total cost for a single API call is the sum of those three parts, while the separate $4.50 / 1M tokens/hour fee is charged for storing the cache between calls.