Block size is rather loaded term, which could mean a number of things:
Smallest addressible unit of data on a hard disk. Also called a sector. Until recently, all hard drives had sector size of 512 bytes. Some current drives have a sector size of 4096 bytes. This parameter is an inherent feature of a drive's hardware and firmware, and cannot be changed.
Smallest addressible unit of data in a filesystem. Also called a cluster. A cluster contains a whole number of disk sectors. The exact size of a cluster is specified during the filesystem creation, e.g. "formatting". Different filesystems support different cluster sizes, however cluster sizes from 4KB to 64KB are most common.
Usually, the default cluster size is the most sensible setting, as the software selects value that is the best trade-off for general filesystem use, taking into an account the size of the filesystem you create.
In conclusion, you can change the cluster size when you reformat your disk (create a new filesystem, wiping everything that was there before), but this is a high-level operation that does not change the sector size which is fixed.
Logical block addressing (LBA)
LBA has nothing to do with this. Older drives used only cylinder-head-sector addressing scheme (CHS). All current drives use just one big number to address sectors on disk, and drive's firmware does the translation of that number to access the needed sector. Then numbers reported by fdisk and similar utilities are "virtual". Your disk does not really have 256 heads, etc.
Low-level formatting is a process of dividing disk tracks into sectors, writing service data, marking bad blocks as such and remapping their contents into a different place on a disk, creating calibration tables, etc. All this activity is done while the drive is still in the factory. This applies to modern drives, which have an integrated disk controller.
Most of the service data on disk is accessible to drive's controller only, some is exposed via SMART etc.
Of course, you can read the zeros that the low-level format wrote all over the disk :-)