នៅក្នុងគណិតវិទ្យា, សមភាពការ៉េទាំង៨របស់ដេហ្គេន ចែងថាផលគុណនៃ២ចំនួនដែលចំនួននីមួយៗជាផលបូកនៃការ៉េនៃ៨ចំនួនផ្សេងទៀត ក៏ជាផលបូកនៃការ៉េនៃ៨ចំនួនដែរ។ មានន័យថា៖
![{\displaystyle (a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+a_{5}^{2}+a_{6}^{2}+a_{7}^{2}+a_{8}^{2})(b_{1}^{2}+b_{2}^{2}+b_{3}^{2}+b_{4}^{2}+b_{5}^{2}+b_{6}^{2}+b_{7}^{2}+b_{8}^{2})=\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e079d20f5fdaacf9a3d0dc9a2991ecb9767ac13)
![{\displaystyle (a_{1}b_{1}-a_{2}b_{2}-a_{3}b_{3}-a_{4}b_{4}-a_{5}b_{5}-a_{6}b_{6}-a_{7}b_{7}-a_{8}b_{8})^{2}+\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f55a0b65cc94ee2635ad945be04655eda53640d6)
![{\displaystyle (a_{2}b_{1}+a_{1}b_{2}+a_{4}b_{3}-a_{3}b_{4}+a_{6}b_{5}-a_{5}b_{6}-a_{8}b_{7}+a_{7}b_{8})^{2}+\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff03602871316079c6c7727e54c256135ef0176f)
![{\displaystyle (a_{3}b_{1}-a_{4}b_{2}+a_{1}b_{3}+a_{2}b_{4}+a_{7}b_{5}+a_{8}b_{6}-a_{5}b_{7}-a_{6}b_{8})^{2}+\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b6682e9355a846d8a15e123524971bfaad8e1fd5)
![{\displaystyle (a_{4}b_{1}+a_{3}b_{2}-a_{2}b_{3}+a_{1}b_{4}+a_{8}b_{5}-a_{7}b_{6}+a_{6}b_{7}-a_{5}b_{8})^{2}+\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ea103044cc55941074043631738a75e31805216e)
![{\displaystyle (a_{5}b_{1}-a_{6}b_{2}-a_{7}b_{3}-a_{8}b_{4}+a_{1}b_{5}+a_{2}b_{6}+a_{3}b_{7}+a_{4}b_{8})^{2}+\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/03ae1f73da3d9b5827233aee5ee959a82018902b)
![{\displaystyle (a_{6}b_{1}+a_{5}b_{2}-a_{8}b_{3}+a_{7}b_{4}-a_{2}b_{5}+a_{1}b_{6}-a_{4}b_{7}+a_{3}b_{8})^{2}+\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60404efd4ea1261d5d010a35c21d067c4adc7896)
![{\displaystyle (a_{7}b_{1}+a_{8}b_{2}+a_{5}b_{3}-a_{6}b_{4}-a_{3}b_{5}+a_{4}b_{6}+a_{1}b_{7}-a_{2}b_{8})^{2}+\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4a2f373e6090fd7ffd2d82b8f5a64ff72a4d960a)
![{\displaystyle (a_{8}b_{1}-a_{7}b_{2}+a_{6}b_{3}+a_{5}b_{4}-a_{4}b_{5}-a_{3}b_{6}+a_{2}b_{7}+a_{1}b_{8})^{2}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d1129c75bc62003e01422319e7ee1be6b02f1bf)
សមភាពនេះត្រូវបានរកឃើញដំបូងដោយ ហ្វែរឌីណាន់ ដេហ្គេន (Ferdinand Degen) នៅឆ្នាំ ១៨១៨។ សមភាពនេះត្រូវបានរកឃើញឡើងវិញដោយឡែកដោយចន ថូម៉ាស់ ហ្គ្រេវ (John Thomas Graves ) (១៨៤៣) និង អារសឺ ខេយឡេយ (Arthur Cayley) (១៨៤៥)