I learned this shortcut from working at the network deployment position. It helped me so much, I figured I will share this secret with everyone. So far, I have not able to find an easier way online that I know of.
For example a network 192.115.103.64 /27, what is the range?
just remember that subnet mask is 0, 128, 192, 224, 240, 248, 252, 254, 255
255.255.255.255 11111111.11111111.11111111.11111111 /32
255.255.255.254 11111111.11111111.11111111.11111110 /31
255.255.255.252 11111111.11111111.11111111.11111100 /30
255.255.255.248 11111111.11111111.11111111.11111000 /29
255.255.255.240 11111111.11111111.11111111.11110000 /28
255.255.255.224 11111111.11111111.11111111.11100000 /27
255.255.255.192 11111111.11111111.11111111.11000000 /26
255.255.255.128 11111111.11111111.11111111.10000000 /25
255.255.255.0 11111111.11111111.11111111.00000000 /24
from /27 we know that (11111111.11111111.11111111.11100000). Counting from the left, it is the third number from the last octet, which equal 255.255.255.224 subnet mask. (Don't count 0, 0 is /24) so 128, 192, 224..etc
Here where the math comes in:
use the subnet mask - subnet mask of the previous listed subnet mask in this case 224-192=32
We know 192.115.103.64 is the network: 64 + 32 = 96 (the next network for /27)
which means we have .0 .32. 64. 96. 128. 160. 192. 224. (Can't use 256 because it is .255)
Here is the range 64 -- 96.
network is 64.
first host is 65.(first network +1)
Last host is 94. (broadcast -1)
broadcast is 95. (last network -1)