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Diffuse the 64 bit key into eight 8 bit blocks. Each block can be brute forced in 2^8 steps. Thus, eight 2^8 steps and in total 2^11 steps are required for brute forcing. Is this kind of brute force possible?

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    $\begingroup$ Could you be more specific? What algorithm are you talking about? In general, this is not a valid strategy for finding e.g. a block cipher key. $\endgroup$ – DiscobarMolokai Mar 8 '17 at 11:07
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No.
This doesn't work like this.
While, yes you can split a 64-bit key up into 8 8-bit blocks, you cannot confirm your sub-block individually. So you can only confirm the entire 64-bit key at once and only get a "yes" or "no" answer.

From this it follows that the maximal time to cracka 64-bit key is indeed $2^{64}$, where you first try all your guesss for the first byte, then all your guesses for the second byte for all your guesses for the first one and so on...

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