Yes, you can absolutely grow a small raspberry bush in an outdoor plant box! Raspberries are versatile plants that adapt well to container gardening, making them a great choice for small spaces like balconies, patios, or urban gardens. Here’s how to do it successfully:

1. Choose the Right Variety: Opt for dwarf or compact raspberry varieties, such as 'Raspberry Shortcake' or 'Baby Cakes,' which are bred specifically for small spaces.

2. Select a Suitable Plant Box: Ensure the container is at least 18-24 inches deep and wide to accommodate the roots. Good drainage is critical, so pick a box with holes or add a layer of gravel at the bottom.

3. Use Quality Soil: Raspberries thrive in well-draining, slightly acidic soil (pH 5.5-6.5). A mix of potting soil and compost works well.

4. Provide Sunlight and Water: Place the plant box in a spot with 6-8 hours of sunlight daily. Water consistently to keep the soil moist but not soggy.

5. Prune and Maintain: Regular pruning encourages healthy growth and fruit production. Remove dead canes and thin out overcrowded areas.

With proper care, your outdoor plant box can yield delicious raspberries in just a season or two. Happy gardening!