If you cut a cubic object 4 times, you can potentially get a maximum of 63 pieces.

Here's how you can achieve this:

1. Cut the cubic object once along one of its diagonal axes, creating 2 pieces.
2. Cut each of the 2 pieces created in step 1, once along a diagonal axis perpendicular to the first cut, creating 4 pieces total.
3. Cut each of the 4 pieces created in step 2, once along a diagonal axis perpendicular to the first two cuts, creating 8 pieces total.
4. Cut each of the 8 pieces created in step 3, once along a diagonal axis perpendicular to the first three cuts, creating 16 pieces total.