Wiring Li Ion cells in parallel to make a 3S8P pack
For the first connection you will need a separate battery ballancing and protection circuit for each 8 parallel legs (strings).

Using the second will save a lot of electronics - you can use a single ballancer as long as it is powerful enough. 


  You should be very careful when connecting batteries like that. All
  batteries should be precharged to exactly the same voltage otherwise
  very large current will flow to equalize the battery state while connecting them.


The best thing about the second circuit is that you will have a longer battery pack life. Why?

Let's say you've got the following pack:







simulate this circuit &ndash; Schematic created using CircuitLab

After given period of usage the batteries will decrease their capacity one by one but not simultaneously. It is never simultaneously. A failed Laptop battery usualy has one or two failed cells and the others got life for dozens of cycles more. In a series connected battery pack the total capacity of the pack is equal to the capacity of the cell with the less capacity. 
Imagine that the first cells to fail (loose capacity) are Bat1 and Bat5 and their capcity has fallen to 30%, while others are still at 70%. With this connection Bat1 got its parallel support from Bat4 and Bat5 is supported by Bat2. This way your total battery pack capacity will fall to (70+30)/2 = 50%.

Now think about the first circuit - if Bat1 and Bat5 fall to 30% and there is no interconnection between the legs, each leg's capacity will be 30% and the total battery pack capacity will be (30+30)/2=30%.