Why is it so difficult to predict?
Also, battery manufacturers often overstate their cells’ capacity, or express it under extremely idealized circumstances.
Elsewhere in the datasheet (or often printed on the cell itself, in the case of rechargeables), you may find a capacity in mAh (milliamp-hours).
Complicating matters further, the LED driver chips themselves use a tiny bit of current, even when the LEDs themselves are “off.” Each chip needs about 2 mA extra…for a strand of 25, it’s using about 50 mA just in this idle state. You may want to factor this into your estimation. Oh, and we forgot to mention power use for the microcontroller that’s driving all this…about 25 mA or so for an Arduino. So we’ll add about 75 mA to the above estimate: 2100 mAh ÷ 525 mA = 4 hours.
If you have a really nice multimeter with an average current recording mode, it will be your new best friend, because it’s doing this based on actual readings. But this capability is usually present only in high-end meters.
You may also want to add some “engineering overhead” to your estimate. Remember what was said about battery capacity often being idealized. So we’ll de-rate the battery by a bit, let’s assume reality is about 80% of the stated capacity: 2100 mAh × 0.8 = 1680 mAh. 1680 mAh ÷ 525 mA = 3.2 hours.
As you can see, there’s an awful lot of fudging and speculation in this process. This is why we say it’s easiest sometimes just to plug in some batteries and keep an eye on it!