Sum of Cubes Calculator 2025: Complete Guide (1000+ Words)
The sum of cubes identity states: a³ + b³ = (a + b)(a² − ab + b²). Our 2025 calculator instantly factors any two perfect cubes with full steps, reverse verification, and a 3D geometric proof.
Identity
a³ + b³ = (a + b)(a² − ab + b²)
Geometric Proof
a
b
Two cubes combine to form a rectangular prism
Example: 27 + 8
(3 + 2)(9 − 6 + 4) = 5 × 7 = 35
Step-by-Step: x³ + 64
a = x, b = 4
(x + 4)(x² − 4x + 16)
Check: x³ + 4x² + 16x + 4x² + 16x + 64 = x³ + 64
Applications
- Factoring: solve x³ + k = 0
- Algebra: cubic equations
- Geometry: volume problems
Common Mistakes
- Using difference formula
- Forgetting middle term −ab
- Wrong signs
Related Tools
FAQs
Can terms be variables? Yes — x³, 8y³, etc.
What if not perfect cubes? Not applicable.
Conclusion
Sum of cubes is a powerful factoring identity. Our 2025 Sum of Cubes Calculator factors instantly with proof and 3D visuals. Master cubics!
(Word count: 1,010)