test(cost): cover undetailed cache-write remainder billing

Regression for #42663: stale 5m/1h breakdown with a larger total,
already-reconciled details (no double-bill), and mixed 5m+1h remainder.

tests/test_litellm/litellm_core_utils/test_calculate_cache_writing_cost.py

@@ -0,0 +1,66 @@
+"""Regression tests for calculate_cache_writing_cost undetailed remainder (#42663)."""
+
+import pytest
+
+from litellm.litellm_core_utils.llm_cost_calc.utils import calculate_cache_writing_cost
+from litellm.types.utils import CacheCreationTokenDetails
+
+
+def test_calculate_cache_writing_cost_bills_undetailed_remainder_at_5m_rate():
+    """
+    Streamed Anthropic server-tool runs keep the message_start 5m/1h breakdown
+    while cache_creation_input_tokens grows across iterations. Pricing must
+    still bill the undetailed remainder at the 5m rate instead of dropping it.
+    """
+    rate_5m = 3.75e-6
+    rate_1h = 6.0e-6
+    details = CacheCreationTokenDetails(
+        ephemeral_5m_input_tokens=31490,
+        ephemeral_1h_input_tokens=0,
+    )
+
+    # Stale breakdown (message_start only) vs full streamed total.
+    cost = calculate_cache_writing_cost(
+        cache_creation_tokens=184457,
+        cache_creation_token_details=details,
+        cache_creation_cost_above_1hr=rate_1h,
+        cache_creation_cost=rate_5m,
+    )
+    assert cost == pytest.approx(184457 * rate_5m)
+
+    # Already-reconciled details (non-streaming aggregate path) must not double-bill.
+    reconciled = CacheCreationTokenDetails(
+        ephemeral_5m_input_tokens=184457,
+        ephemeral_1h_input_tokens=0,
+    )
+    cost_reconciled = calculate_cache_writing_cost(
+        cache_creation_tokens=184457,
+        cache_creation_token_details=reconciled,
+        cache_creation_cost_above_1hr=rate_1h,
+        cache_creation_cost=rate_5m,
+    )
+    assert cost_reconciled == pytest.approx(184457 * rate_5m)
+
+    # Mixed 5m + 1h with an undetailed remainder.
+    mixed = CacheCreationTokenDetails(
+        ephemeral_5m_input_tokens=1000,
+        ephemeral_1h_input_tokens=2000,
+    )
+    cost_mixed = calculate_cache_writing_cost(
+        cache_creation_tokens=5000,
+        cache_creation_token_details=mixed,
+        cache_creation_cost_above_1hr=rate_1h,
+        cache_creation_cost=rate_5m,
+    )
+    assert cost_mixed == pytest.approx(1000 * rate_5m + 2000 * rate_1h + 2000 * rate_5m)
+
+
+def test_calculate_cache_writing_cost_without_details_uses_total():
+    rate_5m = 3.75e-6
+    cost = calculate_cache_writing_cost(
+        cache_creation_tokens=1000,
+        cache_creation_token_details=None,
+        cache_creation_cost_above_1hr=6.0e-6,
+        cache_creation_cost=rate_5m,
+    )
+    assert cost == pytest.approx(1000 * rate_5m)