"Both which" or "both of which"

The "of" is optional; both constructions are grammatically correct. Note, however, that an article or pronoun is mandatory with "both of." "Both of the techniques" (article), "both of their techniques" (possessive pronoun), "both of these techniques" (demonstrative pronoun), and "both of which" (relative pronoun referring to "techniques") are all acceptable. "Both of techniques", on the other hand, is not.

The reason "both of which" may show up on Google more times than "both which" has to do with rhythm--not grammar. English is said to flow in iambic rhythms, forming a general pattern of alternating weak and strong stresses, much like your heartbeat. The "of," in this case, creates a weak beat separating what would be two strong stresses in "both which."

The question of whether a particular syllable constitutes a strong or weak stress depends on the immediately surrounding context. A pattern that our vocal apparatus has difficulty pronouncing ("both which") will slow things down, resulting in a series of consecutive strong beats (spondaic rhythm), while reversing the pattern of stresses or introducing filler words can create something more iambic ("which both" or "both of which"). Most native speakers of English don't even think about these matters of prosody, but I know from experience that they can be annoying to students learning English. Good writers and speakers develop a sense for how they can shape meaning and emphasis by manipulating speech rhythm.

I am sure the following excerpt from an 'Oxford University Press' book will clear all your doubts:

We can put both (of) before nouns and pronouns. Before a noun with a determiner (for example: the, my, these), both and both of are both possible.

Both (of) my parents like riding.

She's eaten both (of) the chops.

We can also use both without a determiner.

She's eaten both chops. (=...both of the chops.)

Only both of is possible before a personal pronoun (us, you, them).

Both of them can come tomorrow.

Mary sends her love to both of us.

We can put both after object pronouns.

I've invited them both.

Mary sends us both her love.

I've made you both something to eat.

'Of' is linked to both, not which. In the same way you would say "Both of my brothers like sport".