Data tag parsing failed when using /blockdata within /blockdata

I was trying to make one command block change its own block data to to use the command /blockdata on another command block.

The command I use was:

/blockdata 95 35 70 {Command:"/blockdata 95 35 70 {Command:"/execute @e[name=Frank] ~ ~ ~ /clone 105 42 73 111 39 79 ~-3 ~ ~-3"}"}

The command block output:

[00:14:47] Data tag parsing failed: Unexpected token '/' at: /execute @e[name=Frank] ~ ~ ~ /clone 105 42 73 111 39 79 ~-3 ~ ~-3"}"

I reproduced the problem by placing 3 command blocks in a row with 1 space between each and placed this command into the first command block:

/blockdata ~ ~ ~2 {Command:"/blockdata ~ ~ ~2 {Command:"/say Works"}"}

The output:

[00:23:40] Data tag parsing failed: Unexpected token '/' at: /say Works"}