I have a cement platform edged by wood next to the wall of my home (? purpose). I would like to create a raised bed to grow vegetables there by using cinder blocks (6x8x16) on the 27x60 in. platform. I will line it with 2 layers of landscape fabric to keep the dirt in, but I do not want to have to use any mortar. It is only going to be 2 levels of cinder blocks. Will this be structurally sound without joining the blocks with mortar? Because the platform is cement I can not drive stakes into the ground for added stability.
Just two levels of blocks will be ok without mortar. It's not going to suddenly come crashing down on someone. The only real downside is that you may need to occasionally reset the blocks if they get bumped out of place.
Also, as DA mentioned in the comments, I think your main concern should be making sure that you have good drainage away from the house.
You might consider using exterior caulk adhesive between the block and on the ends, leaving a gap 1/8" of an inch every 2 blocks I the first or bottom layer (course) of block. In the gap apply adhesive only to the top 1/2 of the block to fill the gap and keep the bottom open for elimination of moisture and water. In this lower section try packing it with some tightly rolled pieces of landscape fabric to create a barrier to stop any soil from flushing out the lower gaps.
Above soil the same method above can be used, but rebar "pins" could be added inside the block to help stabilize them from moving. I did this on all the corners of my raised beds and it worked quite well. Be sure to stagger the block with each course upward so as to help increase the stability.