Board layout help: 64-output Mux! (for possible use in 8x8x8 LED Cube)
No, it's not a good idea. First you're using analog multiplexers which have a rather high \$R_{ON}\$, like 125\$\Omega\$. You're passing two levels of them, so that will be 250\$\Omega\$. Nothing to worry about, you could say, I'll need a series resistor for the LED anyway. Right, but you'll also have to drive a high current through it. You're multiplexing 64 LEDs one by one, so that's a 1.6% duty cycle. You'll have to pulse them with high currents to get some light out of them, possibly even high enough to seriously shorten the LED's life.  

A better solution would be a matrix. The columns could be driven by a ULN2803, which can sink high currents. You could switch columns on one at a time, and for the rows set the row outputs high for the LEDs you want to light in the current column. So a row will only drive 1 LED at a time, a column 8 LEDs at a time. Your duty cycle has increased to 12.5%, so you won't need that excessively high peak current anymore. Yet it will still be more than your microcontroller can deliver, so you'll need a PNP transistor for each row.  

Since you'll be driving only 1 column at a time you can use a demultiplexer like a 74HC238, so you'll need only 3 lines for that. Together with 8 row lines that's a total of 11. That would be OK for 64 LEDs, but you'll need 8 of them for the 8x8x8 cube, and that would be costly in microcontroller output.
Solution: use SIPO (Serial In-Parallel Out) shift registers like the 74HC595 for the row data. Cascade them for the 8 matrices, so that you can shift 64 values through them. When the last bit has been shifted in you latch the data and select the column. While the LEDs for this column are on you can already shift in the data for the next column. At the time cue latch the data, and again select the next column.
Alternatively place the 74HC595s in parallel and shift 8 bits simultaneously in them. This will need 8 bits of your microcontroller's I/O instead of just 1, but you won't need 64 shift operations, only 8.

Note: you'll need a ULN2803 per 64 LED matrix; it can't drive 8x8 rows.