Yes you can drink chicken bouillon cubes.
When I'm sick I boil some water and add some chicken bouillon cubes to the boiling water and make a good chicken broth drink.
Just like you can add the chicken bouillon cubes to your recipes you can drink the chicken broth made from the bouillon cubes as well.
You can also add some parsley or herbs to the broth and make it even healthier.
I love to also drink chicken broth warmed up during cold weather and it's healthy for you.
While chicken broth from the bouillon cubes will not cure a cold or other illness the chicken broth from the bouillon cubes can provide you with nutrients and help you feel better sooner.