The relationship between Goddess Cubes and Chests

It's a Goddess Wall. It just provides you an opportunity to get some free stuff: hearts, rupies, bombs, arrows or fairies. You have to draw certain shapes on the wall in order to choose what you want in one stroke. To initiate it, you need to find a wall, stand in front of it and charge for a Skyward Strike.

Sheikah Stones and other characters will give you hints at what you need to draw.

There are 5 different things you can draw that the game will recognize, otherwise you will get the default 3 hearts.

1.  

   You can draw a heart to get hearts.
   

2.  

   You can draw a rupee to get rupees.
   

3.  

   You can draw a circle to get bombs.
   

4.  

   You can draw an arrow to get arrows.
   

5.  

   You can draw the Triforce to get fairies.
   

Just a warning if you have a widescreen TV with widescreen settings enabled on your Wii, apparently the game doesn't compensate for the stretching that is needed to maintain the correct aspect ratio. So when drawing on the Goddess Walls, I recommend you turn that off temporarily, otherwise you'll have a hard time drawing respectable lines.

You won't be able to access them yet. The earliest you can would be your second visit to the forest...

after you have obtained the Water Dragon's Scale allowing you to swim. You'll have to climb the tree from the inside so you could drop down and reach those cubes.

The target you are referring to is a target for the Clawshots. These come even later in the game and allows you to zoom up to the target.

These are obtained by passing the second goddess trial.