News report from the source: https://www.bls.gov/news.release/cpi.nr0.htm
CPI data series: https://data.bls.gov/timeseries/CUSR0000SA0
CORE CPI data series: http://data.bls.gov/timeseries/CUSR0000SA0L1E
I annualize everything to be comparable to each other and to compare to the Fed's 2% target
They are calculated using the actual index values, not from the rounded off monthly change numbers.
The CPI rise averaged 3.5% over the past 3 months on an annualized basis (core CPI: 3.6%)
The August one month increase annualized is: CPI: 4.7%, (core CPI: 4.2%)
The 12-month average (year-over-year) increase is: CPI: 2.9%, (core CPI: 3.1%)
REGULAR CPI

CORE CPI

Both the CPI and Core CPI 3 month rolling average were hurt when the small May increase dropped out of the 3-month window
The Year - over - year CPI and Core CPI from the OP
So that all the graphs are together

The 12 months averages were hurt by last year's relatively small August 2024 month-over-month increases dropping out of the 12 month window. What drops out of the window is just as important as what enters the 12 month window (which is the latest, August 2025).
Some featured items from the BLS news summary https://www.bls.gov/news.release/cpi.nr0.htm
Increases in August over July:
Shelter: +0.4%, Energy: +0.7% (was -1.1%), Gasoline: +1.9% (was -2.2%),
Food: 0.5% (was 0.0%) and food at home: +0.6% (was -0.1%),, Food away from home: +0.3% (was +0.3%)
The "was" numbers in ( )'s are July over June
In most of these, it was like the August increase is making up for the July decreases or very small increases
12 month increases:
Energy: +0.2%, Food: +3.2%