We present an extension of the Hardy-Littlewood inequality for multilinear forms. More precisely, let K be the real or complex scalar field and m, k be positive integers with m ≥ k and n 1 , . . . , n k be positive integers such that n 1 + · · · + n k = m.T for all m-linear forms T : ℓ n p × · · · × ℓ n p → K and all positive integers n. Moreover, the exponent max 2kp−kpr−pr+2rm 2pr , 0 is optimal.T for all m-linear forms T : ℓ n p × · · · × ℓ n p → K and all positive integers n. Moreover, the exponent max p−rp+rm pr , 0 is optimal. The case k = m recovers a recent result due to G. Araujo and D. Pellegrino.