If you have a sparse melody line on piano a great way to expand your sound can be to add some octaves in the empty places. First, let's consider for a moment that space (silence, rests) in your music is a great thing. It can add atmosphere. It can draw attention to the parts that are being played (after the silence) and it can allow for other instruments to be focused on. So don't think that you need to fill up every gap in your playing on every song. That said, let's take a look at creatively using octaves to enhance your playing.
The piece of music shown here is a one hand piano lesson using octaves and melody. The key of today's lesson is C sharp minor. We chose this to avoid an easy piano key and to get a lot of interaction between white and black keys. Consider the chord for each bar a C# minor. Play this entire piece with your right hand only. You'll notice a triplet group of notes starts each bar. The remaining quarter notes are octaves. The exact same octave pattern ends each bar (B - C# - B).
The triplets are all notes taken from the C# minor scale. The triplets are ascending groups of notes where the approach is more theoretical than musical, but it does sound good. These notes also give your all your fingers a nice workout. You should be able to play this piece of music with minimal hand movement.
If you want to do more with this idea try it out in different keys. Swap it around. Play the octaves first and the melody second. You could also play octaves on beats 1, 3, 4 (or 4 & instead of 3,4) using some tastefully chosen octaves as lead-ins to the next bar (especially if you use a different chord for each bar). Vary your melody notes according to what sounds good to you.
When you come up with an idea you like add some chords or something bassy with your other hand. Have fun.