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Yes, we have to include .

We know ,  size of TAG directory = (No of TAG bit + additional bit)* number of lines in cache
And Size of cache tag directory = Size of tag directory  * Number of tag entries

if we assume, Total cache size = 256 KB 
Cache block size = 32 Bytes 
then, number of cache entries = 256 K / 32 = 8 K = Number of tag entries

 Each Cache Tag Directory entry contains  :

Address tag bits +   valid bits+  modified bits+  replacement bits = Entry size

And  Size of Cache directory =No.of Cache Blocks * Entry size 

so we have to include tag directory size in cache size .

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